Dissertations / Theses: 'MODELO DE LOTKA-VOLTERRA'

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Azevedo, Franciane Silva de. "Modelo de competição de Lotka-Volterra com difusão apliacado a fragmentos de florestas bidimensionais /." São Paulo, 2008. http://hdl.handle.net/11449/132530.

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Orientador: Roberto André Kraenkel
Banca: Fernando Fagundes Ferreira
Banca: Gustavo Camelo Neto
Resumo: Este trabalho estuda equações de reação de difusão em domínios ﬁnitos com vista a aplicações no estudo do efeito de fragmentação de ﬂorestas sobre a dinâmica de populaçõs de espécies. Referimo-nos a habitats de tamanho ﬁnito como sendo habitats insulares. A imensa quantidade de dados observacionais relacionados às espécies biológicas presentes em ilhas ou fragmentos de ﬂorestas motiva este estudo. Mais especiﬁcamente, este trabalho tem como objetivo modelar a dinâmica de interaçãao espacial entre espécies invasoras e espécies nativas de palmeiras, em fragmentos de ﬂoresta amazônica, mostrando que os menores fragmentos são mais suscetíveis a espécies invasoras que os fragmentos maiores. O modelo apresentado é um sistema de equações de competição de Lotka-Volterra, com difusão
Abstract: The present work studies reaction-diﬀusion equations in ﬁnite domains, in view of application to the modeling of the eﬀects of fragmentation on the dynamics of biological species. We refer to ﬁnite habitats as being insular habitats. The great amount of observational data related to biological species in islands or forest fragments motivates this work. More speciﬁcally, this work has as its objective to model the dynamics of the spatial interaction between invader and native species of palm trees in fragments of the Amazon Forest, showing that the smaller fragments are more vulnerable to the invader species than larger fragments. The mathematical model is a system of Lotka-Volterra equations with diﬀusion
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GUTIERREZ, GOMEZ GABRIELA. "RELACIÓN CAPITAL-TRABAJO EN EL MODELO DE LOTKA-VOLTERRA. CASO MEXICANO, 2000-2015." Tesis de Licenciatura, UNIVERSIDAD AUTONOMA DEL ESTADO DE MEXICO, 2017. http://hdl.handle.net/20.500.11799/68005.

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El bajo crecimiento económico es uno de los problemas que más aquejan a las economías del mundo, ya que además de determinar la producción de bienes y servicios de un país durante un período de tiempo determinado, también representa un aspecto fundamental para el desarrollo de cada nación. De acuerdo con lo dicho por Schumpeter (1912), el desarrollo económico es un proceso continuo de crecimiento de la economía durante el cual se aplican nuevas tecnologías a los procesos productivos y a otros campos a los que les sucede cambios institucionales, sociales y políticos, por tanto, desarrollo implica crecimiento económico sostenido (de la Paloma, Maeztu & Gargallo, 2011). En este sentido, la teoría del crecimiento económico, que se ocupa principalmente de analizar los factores que influyen en el ritmo al que crece una economía (Uxó, 2016), considera que los factores de producción con mayor influencia en el comportamiento del crecimiento económico son el capital y el trabajo, dada su presencia y participación en cualquier economía del mundo. México, al tener una economía altamente globalizada por su apertura comercial, está expuesto ante fenómenos de la economía mundial como la volatilidad del tipo de cambio, movimientos en las tasas de interés, fluctuaciones en los precios de las materias primas, entre otros; razón por la que es del interés propio investigar si a través de un modelo dinámico como el de Lotka-Volterra puede explicarse la relación capital-trabajo en la economía mexicana. Resulta importante exponer el panorama general de las variables capital-trabajo en contexto actual. A continuación se hace un análisis deductivo (a nivel mundial, regional y nacional) del capital y el trabajo en el periodo 2000-2015.

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Azevedo, Franciane Silva de [UNESP]. "Modelo de competição de Lotka-Volterra com difusão apliacado a fragmentos de florestas bidimensionais." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/132530.

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Alvarez, Robinson Franco. "Dinâmica de gliomas e possíveis tratamentos." reponame:Repositório Institucional da UFABC, 2016.

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Orientador: Prof. Dr. Roberto Venegeroles Nascimento
Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2016.
Neste trabalho se estudaram aspectos básicos relacionados com a dinâmica de células cancerígenas do tipo B-Linfoma BCL1 e de gliomas fazendo ênfases neste último caso. O trabalho se iniciou revisando alguns modelos populacionais do câncer inspirados nos trabalhos de Lotka e Volterra o qual oferecem uma descrição muito simples da interação entre o câncer (presa) e o sistema imunológico (caçador). Posteriormente é revisado um modelo global espaço-temporal baseado nas equações de Fisher-Kolmogorov-Petrovsky- Piskounov (FKPP) [1] o qual permitiu aclarar a dicotomia entre proliferação e motilidade associada fortemente ao crescimento tumoral e à invasividade, respectivamente, das células cancerosas. A partir do modelo FKPP também se fez um estudo computacional mais detalhado aplicando diferentes protocolos de tratamentos para analisar seus efeitos sobre o crescimento e desenvolvimento de gliomas. O estudo sugere que um tratamento com maior tempo entre cada dose poderia ser mais ótimo do que um tratamento mais agressivo. Propõe-se também um modelo populacional local do câncer em que se tem em conta o caráter policlonal das células cancerígenas e as interações destas com o sistema imunológico natural e especifico. Neste último modelo se consegui apreciar fenômenos como dormancy state (estado de latência) e escape phase (fase de escape) para valores dos parâmetros correspondentes ao câncer de tipo B-Linfoma BCL1 [2] o qual explica os fenômenos de imunoedição e escape da imunovigilância [3] o qual poderia permitir propor novos protocolos de tratamentos mais apropriados.Depois se fez uma reparametrização do modelo baseado em algumas características mais próprias das células tumorais do tipo glioma e assumindo presença de imunodeficiência com o que se obtém coexistências oscilatórias periódicas tanto da população tumoral assim como das células do sistema imunológico o qual poderia explicar os casos clínicos de remissão e posterior reincidência tumoral. Finalmente se obtiveram baixo certas condições, uma dinâmica caótica na população tumoral o qual poderia explicar os casos clínicos em que se apresentam falta de controlabilidade da doença sobre tudo em pessoas idosas ou com algum quadro clinico que envolve alguma deficiência no funcionamento normal do sistema imunológico.
In this work we studied basic aspects of the dynamics of cancer cell type B-Lymphoma BCL1 and gliomas making strong emphasis in the latter case. We start reviewing some population models of cancer inspired in the work¿s of Lotka and Volterra, which offers a very simple description of the interaction between cancer (prey) and the immune system (Hunter). Subsequently revise a global model space-time based on the equations of Fisher-Kolmogorov-Petrovsky-Piskounov (FKPP) [1] which allowed elucidating the dichotomy between proliferation and strongly associated motility to tumor growth and invasiveness, respectively, of cancer cells. From the FKPP model also made a more detailed computer study applying different treatment protocols to analyze their effects on the growth and development of gliomas. The study suggests that treatment with longer time between each dose could be more optimal than a more aggressive treatment. Is studied also a local population cancer model that takes into account the polyclonal nature of cancer cells, and these interactions with the natural and specific immune system. In the latter model is able to appreciate phenomena as dormancy state and escape phase for values of parameters corresponding to lymphoma cancer BCL1 [2] which explains the phenomena of immunoediting and tumor escape immuno-surveillance [3] allowing elucidating treatments protocols more appropriate. A re-parameterization was made based on some features of tumor cells glioma type and assuming presence of immunodeficiency with that obtained coexistences periodic oscillatory both tumor populations as well as the immune system cells which could explain the clinical cases of remission and subsequent tumor recurrence. Finally obtained under certain conditions, a chaotic dynamics in tumor population which could explain the clinical cases that present lack of controllability of the disease on all in elderly or with some clinical picture involving some deficiency in the normal functioning of the immune system.

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Balbín, Arias Julio José. "Formación de patrones inducidos por un flujo de corte en el modelo de Lotka-Volterra modificado." Master's thesis, Pontificia Universidad Católica del Perú, 2017. http://tesis.pucp.edu.pe/repositorio/handle/123456789/8504.

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En esta tesis se analiza la formación de patrones debido a inestabilidades en un sistema de reacción - difusión - advección generadas mediante un flujo de corte. Las inestabilidades son similares a la formación de patrones de Turing en un sistema de activador - inhibidor donde una condición necesaria es que la difusividad del inhibidor es mayor que la difusividad del activador. En presencia de un flujo de corte, nosotros encontramos que esta condición no es necesaria. Nosotros analizamos dos modelos para un flujo de corte, uno de ellos consiste en dos capas moviéndose con diferentes velocidades, el otro correspondiente a un flujo de Poiseuille dentro de un tubo bidimensional. La inestabilidad aparece cuando la velocidad promedio del flujo aumenta por encima de cierta velocidad umbral, conduciendo así a los patrones que se mueven según el marco de referencia del flujo. Nuestros resultados, patrones aislados de Turing, pueden ser obtenidos usando una difusividad efectiva por efecto de la dispersión de Taylor.
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Vérri, Juliano Aparecido. "Estabilidade global e bifurcação de Hopf em um modelo de HIV baseado em sistemas do tipo Lotka-Volterra /." Presidente Prudente, 2013. http://hdl.handle.net/11449/94327.

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Orientador: Marcelo Messias
Banca: Luis Fernando de Osório Mello
Banca: Vanessa Avansini Botta Pirani
Resumo: Nesta dissertação fazemos um estudo de modelos biológicos do tipo Lotka-Volterra, utilizando como ferramenta principal a teoria qualitativa das equações diferenciais ordinárias. Abordamos, no plano e no espaço, alguns modelos do tipo predador-presa. Analisamos os comportamentos das soluções sob a variação dos parâmetros e tratamos com detalhes a bifurcação de Hopf, que dá origem a uma órbita periódica isolada (ciclo limite). Estudamos também um teorema devido a Li e Muldowney [16] sobre a estabilidade global de um ponto de equilíbrio para um sistema x˙ = f(x), x ∈ Rn. Aplicamos este resultado no estudo de um modelo de HIV tridimensional, provando a estabilidade global de um ponto de equilíbrio, para certos valores dos parâmetros. Para o mesmo modelo, verificamos a ocorrência de uma dupla bifurcação de Hopf, que leva ao surgimento e posterior desaparecimento de um ciclo limite, ao variarmos um dos parâmetros envolvidos no sistema. As bifurcações de Hopf ocorrem simultaneamente à perda de estabilidade global do ponto de equilíbrio
Abstract: In this work we present a study of biological models of Lotka-Volterra type, using as main tool the qualitative theory of ordinary differential equations. We analyze some two and three dimensional predator-prey models. The behavior of the solutions are studied under the variation of parameters and it is shown that a Hopf bifurcation occurs, leading to the creation of an isolated periodic orbit (limit cycle). We also study a theorem due to Li and Muldowney [16] about the global stability of an equilibrium point of a system x˙ = f(x), x ∈ Rn. We apply this result in the analysis of a three dimensional model of HIV with treatment, showing the global stability of an equilibrium point, for certain parameter values. For the same model, we prove the occurrence of two Hopf bifurcations, leading to the birth and subsequent death of a limit cycle, when we vary one of the parameters of the model. The Hopf bifurcations occurs simultaneously to the lack of global stability of the equilibrium point
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Vérri, Juliano Aparecido [UNESP]. "Estabilidade global e bifurcação de Hopf em um modelo de HIV baseado em sistemas do tipo Lotka-Volterra." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/94327.

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Nesta dissertação fazemos um estudo de modelos biológicos do tipo Lotka-Volterra, utilizando como ferramenta principal a teoria qualitativa das equações diferenciais ordinárias. Abordamos, no plano e no espaço, alguns modelos do tipo predador-presa. Analisamos os comportamentos das soluções sob a variação dos parâmetros e tratamos com detalhes a bifurcação de Hopf, que dá origem a uma órbita periódica isolada (ciclo limite). Estudamos também um teorema devido a Li e Muldowney [16] sobre a estabilidade global de um ponto de equilíbrio para um sistema x˙ = f(x), x ∈ Rn. Aplicamos este resultado no estudo de um modelo de HIV tridimensional, provando a estabilidade global de um ponto de equilíbrio, para certos valores dos parâmetros. Para o mesmo modelo, verificamos a ocorrência de uma dupla bifurcação de Hopf, que leva ao surgimento e posterior desaparecimento de um ciclo limite, ao variarmos um dos parâmetros envolvidos no sistema. As bifurcações de Hopf ocorrem simultaneamente à perda de estabilidade global do ponto de equilíbrio
In this work we present a study of biological models of Lotka-Volterra type, using as main tool the qualitative theory of ordinary differential equations. We analyze some two and three dimensional predator-prey models. The behavior of the solutions are studied under the variation of parameters and it is shown that a Hopf bifurcation occurs, leading to the creation of an isolated periodic orbit (limit cycle). We also study a theorem due to Li and Muldowney [16] about the global stability of an equilibrium point of a system x˙ = f(x), x ∈ Rn. We apply this result in the analysis of a three dimensional model of HIV with treatment, showing the global stability of an equilibrium point, for certain parameter values. For the same model, we prove the occurrence of two Hopf bifurcations, leading to the birth and subsequent death of a limit cycle, when we vary one of the parameters of the model. The Hopf bifurcations occurs simultaneously to the lack of global stability of the equilibrium point

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Griebeler, Marcelo de Carvalho. "Ensaios em política e desenvolvimento econômico." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2013. http://hdl.handle.net/10183/87327.

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Esta tese é composta por três ensaios. No primeiro, mostramos em nosso modelo básico que economias formadas exclusivamente por produtores e parasitas podem cair em armadilhas de pobreza, desde que ambos grupos se comportem de acordo com a dinâmica de Lotka-Volterra. Contudo, a introdução de um limite para o crescimento do produto e de expectativas por parte dos agentes exclui o resultado de armadilha em seus múltiplos equilíbrios. Nossa conclusão, entretanto, é similar para ambos modelos estudados: melhora na proteção aos direitos de propriedade por parte do Estado pode fazer com que a armadilha de pobreza seja superada, no modelo básico; e afetar a estabilidade dos equilíbrios, no modificado, fazendo com que resultados econômicos com maior produto tornem-se estáveis. No segundo ensaio, obtemos condições sob as quais a função perda do banco central é estritamente convexa em quatro estados distintos da economia: economia aquecida, em recessão, inação alta e produto alto. Encontramos, ainda, que quando in- ação e produto são funções lineares do instrumento de política monetária, a convexidade é garantida para qualquer um dos quatro estados citados. Ao estendermos nossa análise a vários instrumentos, encontramos que apenas linearidade já não é mais suficiente para a garantia do formato da função perda. Nossos resultados fornecem, ainda, condições sob as quais existirá dependência entre os instrumentos de política monetária. Por fim, o terceiro ensaio estuda regimes de metas de inação, nos quais agentes podem influenciar a política monetária através das expectativas de mercado reportadas ao banco central. Este, por sua vez, deve formular a política monetária considerando que tal influência pode ser usada em benefício dos próprios agentes. Modelamos essa relação estratégica como um jogo sequencial entre uma instituição financeira representativa e o banco central. Mostramos que quando a autoridade monetária escolhe apenas o nível da taxa de juros, existe um potencial viés inflacionário na economia. Esse viés é superado quando a oferta de moeda torna-se um segundo instrumento de política. Ainda mostramos que penalização de instituições más previsoras também pode ser um mecanismo eficiente de ancoragem de expectativas.
This thesis consists of three essays. In the first one, we show in our basic model that economies consisted exclusively by producers and parasites may fall into poverty traps, assuming that both groups behave according to the dynamics of Lotka-Volterra. However, the introduction of an upper bound on the output growth and expectations for the agents excludes the result of trap in its multiple equilibria. Our conclusion, nevertheless, is similiar for both studied models: improved protection of property rights by the state can mitigate the poverty trap possibility in the basic model, and affect the stability of equilibria in the modified one, making that economic outcomes with higher output become stable. In the second essay, we obtain conditions under which the central bank's loss function is strictly convex in four different states of the economy: booming economy, recession, high inflation and high output. Moreover, we found that when inaction and output are linear functions of monetary policy instruments, convexity is guaranteed for any of the four states mentioned. When we extend our analysis to the case of many instruments, we found that only linearity is not sufficient to guarantee the shape of loss function. Our results also provide conditions under which there exists dependence between instruments of monetary policy. Finally, the third essay studies the ination targeting regimes, in which agents can influence the monetary policy through market expectations reported to the central bank. Monetary authority, in its turn, should formulate the monetary policy considering that this influence may be used for the benefit of agents themselves. We model this strategic relationship as a sequential game between a representative financial institution and the central bank. We show that when the monetary authority chooses only the level of interest rates, there is a potential inflationary bias in the economy. This bias is solved when the money supply becomes a second instrument of policy. In addition, we show that to impose penalty on the worse predictor institutions may also be an efficient anchoring expectations mechanism.

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Alzahrani, Ebraheem. "Travelling waves in Lotka-Volterra competition models." Thesis, University of Dundee, 2011. https://discovery.dundee.ac.uk/en/studentTheses/1e432558-a3eb-40ee-81ae-4f0af74718d0.

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In this thesis, we study a class of multi-stable reaction-diffusion systems used to model competing species. Systems in this class possess uniform stable steady states representing semi-trivial solutions. We start by considering a bistable, interaction, where the interactions are of classic “Lotka-Volterra” type and we consider a particular problem with relevance to applications in population dynamics: essentially, we study under what conditions the interplay of relative motility (diffusion) and competitive strength can cause waves of invasion to be halted and reversed. By establishing rigorous results concerning related degenerate and near-degenerate systems,we build a picture of the dependence of the wave speed on system parameters. Our results lead us to conjecture that this class of competition model has three “zones of response” in which the wave direction is left-moving, reversible and right-moving, respectively and indeed that in all three zones, the wave speed is an increasing function of the relative motility. Moreover, we study the effects of domain size on planar and non-planar interfaces and show that curvature plays an important role in determining competitive outcomes. Finally, we study a 3-species Lotka-Volterra model, where the third species is treated as a bio-control agent or a bio-buffer and investigate under what conditions the third species can alter the existing competition interaction.

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Chen, Sheng. "Population dynamics of stochastic lattice Lotka-Volterra models." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/82038.

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In a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions and subject to occupation restrictions, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. When investigating the non-equilibrium relaxation of the predator density in the vicinity of the phase transition point, we observe critical slowing-down and algebraic decay of the predator density at the extinction critical point. The numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population's proximity to its extinction threshold. In order to study boundary effects, we split the system into two patches: Upon setting the predation rates at two distinct values, one half of the system resides in an absorbing state where only the prey survives, while the other half attains a stable coexistence state wherein both species remain active. At the domain boundary, we observe a marked enhancement of the predator population density, the minimum value of the correlation length, and the maximum attenuation rate. Boundary effects become less prominent as the system is successively divided into subdomains in a checkerboard pattern, with two different reaction rates assigned to neighboring patches. We furthermore add another predator species into the system with the purpose of studying possible origins of biodiversity. Predators are characterized with individual predation efficiencies and death rates, to which "Darwinian" evolutionary adaptation is introduced. We find that direct competition between predator species and character displacement together play an important role in yielding stable communities. We develop another variant of the lattice predator-prey model to help understand the killer- prey relationship of two different types of E. coli in a biological experiment, wherein the prey colonies disperse all over the plate while the killer cell population resides at the center, and a "kill zone" of prey forms immediately surrounding the killer, beyond which the prey population gradually increases outward.
Ph. D.

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Artioli, Simone. "Dinamica delle popolazioni: modelli deterministici di Lotka-Volterra." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21934/.

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Lo scopo di questo lavoro di tesi è quello di analizzare i modelli deterministici di dinamica delle popolazioni, dal primo e più semplice modello Malthusiano per la descrizione del comportamento dinamico di un insieme di individui considerati pressoché identici, fino ad arrivare allo studio dei sistemi del tipo preda-predatore trattati grazie al famoso modello di Lotka-Volterra. Tale modello è stato studiato nella sua versione base, in cui esso descrive la dinamica di interazione tra due specie compresenti nello stesso ambiente, sia da un punto di vista puramente matematico sia tramite simulazioni numeriche. Successivamente il modello è stato complicato per descrivere in modo migliore sistemi reali in cui non sono disponibili risorse infinite per lo sviluppo degli individui grazie all’utilizzo di un termine derivato dal modello di crescita logistica. Successivamente si è passati allo studio di un’ultima complicazione del modello, trattando i sistemi a più specie, esponendo il costrutto matematico definente tali sistemi, da un punto di vista puramente teorico per il caso ad N specie, mentre invece è stato approfondito il caso particolare del tipo preda-preda-predatore studiandone le proprietà dinamiche è commentando le soluzioni ricavate nuovamente tramite simulazione. Infine, i modelli precedentemente esposti sono stati utilizzati per operare un confronto con alcuni dati provenienti da due ricerche appartenenti a due ambiti scientifici diversi.

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Sanchioni, Stefano. "Stochastic Lotka-Volterra models: neutral and niche theories for biosystems." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18115/.

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In questo lavoro di tesi sono stati studiati modelli stocastici per ecosistemi basati su equazioni di tipo Lotka-Volterra con componenti fluttuanti. E' stato affrontato per primo il modello preda-predatore aggiungendo un rumore additivo ed è stata risolta l'equazione linearizzata attorno all'equilibrio. Con una limitazione alla crescita delle prede e rumore moltiplicativo si è proposto poi un modello più completo di cui si può calcolare la distribuzione di probabilità all'equilibrio. Nel caso deterministico si è fatto un confronto con dati raccolti sull’Isle Royale. Il secondo passo è stato quello di considerare specie in competizione, nell'ambito delle teorie di nicchia, e le fluttuazioni dovute alla scarsa numerosità in presenza di immigrazione, nell'ambito delle teorie neutrali. La master equation è stata analizzata in dettaglio per una popolazione con crescita limitata e immigrazione. Il passaggio da una distribuzione Gaussiana a quella di Pareto mostra come sia cruciale la scelta della forma della fluttuazione. La teoria di nicchia è stata sviluppata per due popolazioni a crescita limitata in competizione tra loro e con immigrazione, studiando gli equilibri, la loro stabilità e le biforcazioni nel caso deterministico. Si è anche indicato come formulare la master equation per combinare teoria neutrale e di nicchia in un unico modello, come proposto da Haegeman. Si è infine delineato il caso più generale di N specie, composte sia da prede in competizione sia da predatori, presenti nello stesso ambiente. Si è studiato in dettaglio un ecosistema costituito da due prede e un predatore senza competizione tra le prede caratterizzando completamente gli equilibri e la loro natura. Un confronto con dati empirici su microrganismi ha mostrato un ottimo accordo con le predizioni del modello, aprendo la possibilità per una sua estensione che includa la competizione tra le prede al fine di descrivere anche il comportamento caotico osservato sperimentalmente.

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Ünver, Hakkı Özgür. "A comparative study of Lotka-Volterra and system dynamics models for simulation of technology industry dynamics." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44705.

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Thesis (S.M.)--Massachusetts Institute of Technology, System Design and Management Program, 2008.
Includes bibliographical references (leaves 78-80).
Scholars have developed a range of qualitative and quantitative models for generalizing the dynamics of technological innovation and identifying patterns of competition between rivals. This thesis compares two predominant approaches in the quantified modeling of technological innovation and competition. Multi-mode framework, based on the Lotka-Volterra equation barrowed from biological ecology, provide a rich setting for assessing the interaction between two or more technologies. A more recent approach uses System Dynamics to model the dynamics of innovative industries. A System Dynamics approach enables the development of very comprehensive models, which can cover multiple dimensions of innovation, and provides very broad insights for innovative and competitive landscape of an industry. As well as comparing these theories in detail, a case study is also performed on both of them. The phenomenal competition between two technologies in the consumer photography market; the recent battle between digital and film camera technology, is used as a test case and simulated by both models. Real market data is used as inputs to the simulations. Outputs are compared and interpreted with the realities of the current market conditions and predictions of industry analysts. Conclusions are derived on the strengths and weaknesses of both approaches. Directions for future research on model extensions incorporating other forms of innovation are given, such as collaborative interaction in SME networks.
by Hakkı Özgür Ünver.
S.M.

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Halvorsen, Gaute. "Numerical Solution of Stochastic Differential Equations by use of Path Integration : A study of a stochastic Lotka-Volterra model." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-14421.

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Some theory of real and stochastic analysis in order to introduce the Path Integration method in terms of stochastic operators. A theorem presenting sufficient conditions for convergence of the Path Integration method is then presented. The solution of a stochastic Lotka-Volterra model of a prey-predator relationship is then discussed, with and without the predator being harvested. And finally, an adaptive algorithm designed to solve the stochastic Lotka-Volterra model well, is presented.

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15

Chrobok, Viktor. "Optimization of Harvesting Natural Resources." Doctoral thesis, Vysoká škola ekonomická v Praze, 2008. http://www.nusl.cz/ntk/nusl-196942.

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The thesis describes various modifications of the predator-prey model. The modifications are considering several harvesting methods. At the beginning a solution and a sensitivity analysis of the basic model are provided. The first modification is the percentage harvesting model, which could be easily converted to the basic model. Secondly a constant harvesting including a linearization is derived. A significant part is devoted to regulation models with special a focus on environmental applications and the stability of the system. Optimization algorithms for one and both species harvesting are derived and back-tested. One species harvesting is based on econometrical tools; the core of two species harvesting is the modified Newton's method. The economic applications of the model in macroeconomics and oligopoly theory are expanded using the methods derived in the thesis.

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16

Vassilieva, Olga. "Modeling and Analysis of Population Dynamics in Advective Environments." Thèse, Université d'Ottawa / University of Ottawa, 2011. http://hdl.handle.net/10393/19982.

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We study diffusion-reaction-advection models describing population dynamics of aquatic organisms subject to a constant drift, with reflecting upstream and outflow downstream boundary conditions. We consider three different models: single logistically growing species, two and three competing species. In the case of a single population, we determine conditions for existence, uniqueness and stability of non-trivial steady-state solutions. We analyze the dependence of such solutions on advection speed, growth rate and length of the habitat. Such analysis offers a possible explanation of the "drift paradox" in our context. We also introduce a spatially implicit ODE (nonspatial approximation) model which captures the essential behavior of the original PDE model. In the case of two competing species, we use a diffusion-advection version of the Lotka-Volterra competition model. Combining numerical and analytical techniques, in both the spatial and nonspatial approximation settings, we describe the effect of advection on competitive outcomes. Finally, in the case of three species, we use the nonspatial approximation approach to analyze and classify the possible scenarios as we change the flow speed in the habitat.

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17

Chrobok, Viktor. "Harvesting in the Predator - Prey Model." Master's thesis, Vysoká škola ekonomická v Praze, 2009. http://www.nusl.cz/ntk/nusl-10510.

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The paper is focused on the Predator-Prey model modified in the case of harvesting one or both populations. Firstly there is given a short description of the basic model and the sensitivity analysis. The first essential modification is percentage harvesting. This model could be easily converted to the basic one using a substitution. The next modification is constant harvesting. Solving this system requires linearization, which was properly done and brought valuable results applicable even for the basic or the percentage harvesting model. The next chapter describes regulation models, which could be used especially in applying environmental policies. All reasonable regulation models are shown after distinguishing between discrete and continuous harvesting. The last chapter contains an algorithm for maximizing the profit of a harvester using econometrical modelling tools.

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18

Fiorini, Barbara. "Teoria ed applicazioni delle equazioni differenziali ordinarie." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/5581/.

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19

Wasson, Samantha Rae. "Increasing Introductory Biology Students' Modeling Mastery Through Visualizing Population Growth Models." BYU ScholarsArchive, 2021. https://scholarsarchive.byu.edu/etd/9181.

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In introductory biology, college students are taught to predict how populations will grow and change over time by using population growth models. These models are commonly represented as mathematical equations. However, students consistently struggle when math and biology concepts intersect in the classroom, and these struggles lead to suboptimal understanding of how mathematical population models are designed and used. Education literature suggests that students may struggle with population modeling because of math anxiety, the high cognitive load of the task, and the lack of scaffolding for abstract concepts. In our study, we sought to improve student mastery modeling exponential growth, logistic growth, and Lotka-Volterra predator-prey interactions through using pictorial diagrams in modeling pedagogy. We predicted that these diagrams would reduce the amount of triggered math anxiety, lower the cognitive load of the task through reducing element interactivity, and allow for a more scaffolding for abstract symbols through a pictorial representation bridge. To test the effectiveness of population diagrams, we created two versions of a population modeling lesson plan: one version taught using diagrams then equations, while the other taught using purely equations. We also designed practice and assessment questions that tested calculation and model-building ability. We assessed math anxiety, scientific reasoning ability, and math ability at the beginning of the semester and state anxiety, effort of tasks, and difficulty of tasks during each lesson. Over 200 students from a non-major biology course were randomly assigned to each group, and all were given a pre-assessment, four lessons, a practice test, and a unit test on population modeling. Our findings show that while the addition of pictorial models to the traditional pedagogy did not have a significant effect on exponential and logistic growth model mastery, students that were exposed to predator-prey diagrams were more able to create a new model for a three-level predator-prey interaction than students that were only given traditional pedagogy. In addition, students who were exposed to predator-prey interaction diagrams before they derived equations reported a lower cognitive load than students who were only exposed to equations. Although diagrams were not a more helpful calculation tool for students than traditional equations, using population diagrams before to equation derivation may help improve student mastery of growth model creation.

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20

Vanni, Davide. "Modelli biomatematici differenziali e stocastici." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13641/.

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La previsione dei comportamenti delle malattie infettive e delle popolazioni di animali sono argomenti molto dibattuti e popolari al giorno d'oggi. Sempre più l'uomo tenta di salvaguardare specie animali in via di estinzione e prevedere e prevenire contagi sia umani che di bestiame. I modelli di biomatematica sono uno strumento essenziale per poter prevedere e quindi agire su questi fenomeni. Talvolta, però, i fenomeni naturali sfuggono dalle previsioni matematiche tradizionali, così, sempre più spesso i modelli differenziali vengono affiancati da modelli probabilistici. In questa tesi verranno messi a confronto modelli di biomatematica differenziali e stocastici (catene di Markov a tempo discreto - DTMC), si osserveranno differenze ed analogie tra i due modelli, i loro comportamenti e le loro previsioni mettendole a confronto con dati reali. In particolare si analizzeranno i modelli SIS e SIR a popolazione costante e si utilizzerà il modello SIR per modellizzare e far previsioni su due problemi reali: l'influenza in una scuola inglese e la peste ad Eyam del 1666. Osservando gli errori tra i modelli ed i dati reali si giungerà all'interessante risultato che le modellizzazioni stocastica e differenziale richiedono due parametrizzazioni differenti, secondo il criterio dell'errore quadratico. Si sono quindi introdotte le catene di Markov a tempo continuo ed il poco esplorato settore di modellizzazione tramite esse, specialmente per processi multivariati, e, adattando un teorema di probabilità, si è costruito un algoritmo per simularle tramite calcolatore. In particolare si sono trasposti in CTMC i modelli SIS e SIR e si sono introdotti due ulteriori modelli non realizzabili stocasticamente tramite DTMC: il modello Lotka-Volterra e il modello di "due popolazioni interagenti", evidenziando i loro comportamenti limite tramite simulazioni numeriche.

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21

Zararsiz, Zarife. "On an epidemic model given by a stochastic differential equation." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5747.

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22

Lusuardi, Alice. "Modelli matematici per lo studio di popolazioni interagenti in un ecosistema." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13547/.

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La tesi tratta di alcuni modelli matematici che descrivono l’andamento di una popolazione e l’interazione tra due specie in un ecosistema. Dopo una prima esposizione di alcuni concetti teorici necessari alla comprensione degli argomenti trattati, un primo modello presentato è quello di Malthus. Esso descrive la crescita esponenziale o la decrescita esponenziale di una popolazione. In seguito si è studiato un perfezionamento del modello precedente, il modello logistico, che tiene conto delle risorse ambientali e secondo il quale una popolazione, ad un certo punto, raggiunge una situazione di equilibrio. Infine è stato descritto il modello preda-predatore sulla base delle equazioni di Lotka-Volterra, che spiega l’andamento di due specie interagenti tra loro in un ecosistema. Attraverso questo modello si è arrivati alla conclusione che, ad un picco della numerosità delle prede, segue un picco della numerosità dei predatori.

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23

D'Izzia, Salvatore. "stabilita' delle soluzioni di equazioni differenziali e dinamica delle popolazioni." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020.

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Il contenuto della tesi consiste in definizioni di stabilità nel senso di Lyapunov, classificazione dei punti di equilibrio per sistemi differenziali lineari nel piano, criteri per determinare la stabilità dei punti di equilibrio per sistemi differenziali non necessariamente lineari ed infine si passa all'aspetto applicativo dei risultati esposti.

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24

Jönsson, Ingela, and Mattias Nilsson. "Klassiska populationsmodeller kontra stokastiska : En simuleringsstudie ur matematiskt och datalogiskt perspektiv." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-2262.

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I detta tvärvetenskapliga arbete studeras från den matematiska sidan tre klassiska populationsmodeller: Malthus tillväxtmodell, Verhulsts logistiska modell och Lotka-Volterras jägarebytesmodell. De klassiska modellerna jämförs med stokastiska. De stokastiska modeller som studeras är födelsedödsprocesser och deras diffusionsapproximation. Jämförelse görs med medelvärdesbildade simuleringar.

Det krävs många simuleringar för att kunna genomföra jämförelserna. Dessa simuleringar måste utföras i datormiljö och det är här den datalogiska aspekten av arbetet kommer in. Modellerna och deras resultathantering har implementerats i både MatLab och i C, för att kunna möjliggöra en undersökning om skillnaderna i tidsåtgången mellan de båda språken, under genomförandet av ovan nämnda jämförelser. Försök till tidsoptimering utförs och även användarvänligheten under implementeringen av de matematiska problemen i de båda språken behandlas.

Följande matematiska slutsatser har dragits, att de medelvärdesbildade lösningarna inte alltid sammanfaller med de klassiska modellerna när de simuleras på stora tidsintervall. I den logistiska modellen samt i Lotka-Volterras modell dör förr eller senare de stokastiska simuleringarna ut när tiden går mot oändligheten, medan deras deterministiska representation lever vidare. I den exponentiella modellen sammanfaller medelvärdet av de stokastiska simuleringarna med den deterministiska lösningen, dock blir spridningen stor för de stokastiska simuleringarna när de utförs på stora tidsintervall.

Datalogiska slutsatser som har dragits är att när det kommer till att implementera få modeller, samt resultatbearbetning av dessa, som ska användas upprepade gånger, är C det bäst lämpade språket då det visat sig vara betydligt snabbare under exekvering än vad MatLab är. Dock måste hänsyn tas till alla de svårigheter som implementeringen i C drar med sig. Dessa svårigheter kan till stor del undvikas om implementeringen istället sker i MatLab, då det därmed finns tillgång till en uppsjö av väl lämpade funktioner och färdiga matematiska lösningar.

In this interdisciplinary study, three classic population models will be studied from a mathematical view: Malthus’ growth, Verhulst’s logistic model and Lotka-Volterra’s model for hunter and prey. The classic models are being compared to the stochastic ones. The stochastic models studied are the birthdeath processes and their diffusion approximation. Comparisons are made by averaging simulations.

It requires numerous simulations to carry out the comparisons. The simulations must be carried out on a computer and this is where the computer science emerges to the project. The models, along with the handling of the results, have been implemented in both Mat- Lab and in C in order to allow a comparison between the two languages whilst executing the above mentioned study. Attempts to time optimization and an evaluation concerning the user-friendliness regarding the implementation of mathematical problems will be performed.

Mathematic conclusions, which have been drawn, are that the averaging solutions do not always coincide with the traditional models when they are being simulated over large time. In the logistic model and in Lotka-Volterra’s model the stochastic simulations will sooner or later die when the time is moving towards infinity, whilst their deterministic representation keeps on living. In the exponential model, the mean values of the stochastic simulations and of the deterministic solution coincide. There is, however, a large spread for the stochastic simulations when they are carried out over a large time.

Computer scientific conclusions drawn from the study includes that when it comes to implementing a few models, along with the handling of the results, to be used repeatedly, C is the most appropriate language as it proved to be significantly faster during execution. However, all of the difficulties during the implementation of mathematical problems in C must be kept in mind. These difficulties can be avoided if the implementation instead takes place in MatLab, where a numerous of mathematical functions and solutions will be available.

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25

Piltz, Sofia Helena. "Models for adaptive feeding and population dynamics in plankton." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:811fd94d-d58e-48fa-8848-ad7dc37a099f.

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Traditionally, differential-equation models for population dynamics have considered organisms as "fixed" entities in terms of their behaviour and characteristics. However, there have been many observations of adaptivity in organisms, both at the level of behaviour and as an evolutionary change of traits, in response to the environmental conditions. Taking such adaptiveness into account alters the qualitative dynamics of traditional models and is an important factor to be included, for example, when developing reliable model predictions under changing environmental conditions. In this thesis, we consider piecewise-smooth and smooth dynamical systems to represent adaptive change in a 1 predator-2 prey system. First, we derive a novel piecewise-smooth dynamical system for a predator switching between its preferred and alternative prey type in response to prey abundance. We consider a linear ecological trade-off and discover a novel bifurcation as we change the slope of the trade-off. Second, we reformulate the piecewise-smooth system as two novel 1 predator-2 prey smooth dynamical systems. As opposed to the piecewise-smooth system that includes a discontinuity in the vector fields and assumes that a predator switches its feeding strategy instantaneously, we relax this assumption in these systems and consider continuous change in a predator trait. We use plankton as our reference organism because they serve as an important model system. We compare the model simulations with data from Lake Constance on the German-Swiss-Austrian border and suggest possible mechanistic explanations for cycles in plankton concentrations in spring.

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26

Nilsson, Mattias, and Ingela Jönsson. "Klassiska populationsmodeller kontra stokastiska : En simuleringsstudie ur matematiskt och datalogiskt perspektiv." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-2263.

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Abstract:

I detta tvärvetenskapliga arbete studeras från den matematiska sidan tre klassiska populationsmodeller: Malthus tillväxtmodell, Verhulsts logistiska modell och Lotka-Volterras jägarebytesmodell. De klassiska modellerna jämförs med stokastiska. De stokastiska modeller som studeras är födelsedödsprocesser och deras diffusionsapproximation. Jämförelse görs med medelvärdesbildade simuleringar.

Det krävs många simuleringar för att kunna genomföra jämförelserna. Dessa simuleringar måste utföras i datormiljö och det är här den datalogiska aspekten av arbetet kommer in. Modellerna och deras resultathantering har implementerats i både MatLab och i C, för att kunna möjliggöra en undersökning om skillnaderna i tidsåtgången mellan de båda språken, under genomförandet av ovan nämnda jämförelser. Försök till tidsoptimering utförs och även användarvänligheten under implementeringen av de matematiska problemen i de båda språken behandlas.

Följande matematiska slutsatser har dragits, att de medelvärdesbildade lösningarna inte alltid sammanfaller med de klassiska modellerna när de simuleras på stora tidsintervall. I den logistiska modellen samt i Lotka-Volterras modell dör förr eller senare de stokastiska simuleringarna ut när tiden går mot oändligheten, medan deras deterministiska representation lever vidare. I den exponentiella modellen sammanfaller medelvärdet av de stokastiska simuleringarna med den deterministiska lösningen, dock blir spridningen stor för de stokastiska simuleringarna när de utförs på stora tidsintervall.

Datalogiska slutsatser som har dragits är att när det kommer till att implementera få modeller, samt resultatbearbetning av dessa, som ska användas upprepade gånger, är C det bäst lämpade språket då det visat sig vara betydligt snabbare under exekvering än vad MatLab är. Dock måste hänsyn tas till alla de svårigheter som implementeringen i C drar med sig. Dessa svårigheter kan till stor del undvikas om implementeringen istället sker i MatLab, då det därmed finns tillgång till en uppsjö av väl lämpade funktioner och färdiga matematiska lösningar.

In this interdisciplinary study, three classic population models will be studied from a mathematical view: Malthus’ growth, Verhulst’s logistic model and Lotka-Volterra’s model for hunter and prey. The classic models are being compared to the stochastic ones. The stochastic models studied are the birthdeath processes and their diffusion approximation. Comparisons are made by averaging simulations.

It requires numerous simulations to carry out the comparisons. The simulations must be carried out on a computer and this is where the computer science emerges to the project. The models, along with the handling of the results, have been implemented in both MatLab and in C in order to allow a comparison between the two languages whilst executing the above mentioned study. Attempts to time optimization and an evaluation concerning the user-friendliness regarding the implementation of mathematical problems will be performed.

Mathematic conclusions, which have been drawn, are that the averaging solutions do not always coincide with the traditional models when they are being simulated over large time. In the logistic model and in Lotka-Volterra’s model the stochastic simulations will sooner or later die when the time is moving towards infinity, whilst their deterministic representation keeps on living. In the exponential model, the mean values of the stochastic simulations and of the deterministic solution coincide. There is, however, a large spread for the stochastic simulations when they are carried out over a large time.

Computer scientific conclusions drawn from the study includes that when it comes to implementing a few models, along with the handling of the results, to be used repeatedly, C is the most appropriate language as it proved to be significantly faster during execution. However, all of the difficulties during the implementation of mathematical problems in C must be kept in mind. These difficulties can be avoided if the implementation instead takes place in MatLab, where a numerous of mathematical functions and solutions will be available.

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27

Беляев, А. В., and A. V. Belyaev. "Анализ стохастических моделей живых систем с дискретным временем : магистерская диссертация." Master's thesis, б. и, 2020. http://hdl.handle.net/10995/87578.

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Работа содержит исследования трех моделей живых систем с дискретным временем. В первой главе рассматривается одномерная модель нейронной активности, задаваемая кусочно-гладким отображением. Показывается, что в случае одномерного отображения наличие случайного возмущения приводит к появлению всплесков (спайкингу). Исследуются два механизма генерации спайков, вызванных добавлением случайного возмущения в один из параметров. Иллюстрируется, что сосуществование двух аттракторов является не единственной причиной возникновения спайкинга. Для прогнозирования уровня интенсивности шума, необходимого для генерации спайков, применяется метод доверительных областей, который основан на функции стохастической чувствительности. Также находятся основные характеристики межспайковых интервалов в зависимости от интенсивности шума. Вторая глава работы посвящена применению метода функции стохастической чувствительности к аттракторам кусочно-гладкого одномерного отображения, описывающего динамику численности популяции. Первым этапом исследования является параметрический анализ возможных режимов детерминированной модели: определение зон существования устойчивых равновесий и хаотических аттракторов. Для определения параметрических границ хаотического аттрактора применяется теория критических точек. В случае, когда на систему оказывает влияние случайное воздействие, на основе техники функции стохастической чувствительности дается описание разброса случайных состояний вокруг равновесия и хаотического аттрактора. Проводится сравнительный анализ влияния параметрического и аддитивного шума на аттракторы системы. С помощью техники доверительных интервалов изучаются вероятностные механизмы вымирания популяции под действием шума. Анализируются изменения параметрических границ существования популяции под действием случайного возмущения. В третьей главе проводится анализ возможных динамических режимов детерминированной и стохастической модели Лотки-Вольтерры. В зависимости от двух параметров системы строится карта режимов. Изучаются параметрические зоны существования устойчивых равновесий, циклов, замкнутых инвариантных кривых, а также хаотических аттракторов. Описываются бифуркации удвоения периода, Неймарка--Саккера и кризиса. Демонстрируется сложная форма бассейнов притяжения. Помимо детерминированной системы подробно изучается стохастическая, описывающая влияние внешнего случайного воздействия. В случае хаоса дан алгоритм нахождения критических линий, описывающих границу хаотического аттрактора. Опираясь на найденную чувствительность аттракторов, строятся доверительные полосы и эллипсы, позволяющие описать разброс случайных состояний вокруг детерминированного аттрактора.
The work contains study of three models of biological systems with discrete time. In the first chapter a one-dimensional model of neural activity defined by a piecewise-smooth map is considered. It is shown that in the case of a one-dimensional model, the presence of a random disturbance leads to a spike generation. Two mechanisms of spike generation caused by the presence of a random disturbance in one of the parameters are investigated. It is illustrated that the coexistence of two attractors is not the only reason of spiking. To predict the level of noise intensity needed to generate spikes, the confidence-domain method is used, which is based on the stochastic sensitivity function. The main characteristics of interspike intervals depending on the intensity of the noise are also described. The second chapter is devoted to the application of the method of the stochastic sensitivity function to attractors of a piecewise-smooth one-dimensional map, which describes the population dynamics. The first stage of the study is a parametric analysis of the possible regimes of the deterministic model: determining the zones of existence of stable equilibria and chaotic attractors. The theory of critical points is used to determine the parametric boundaries of a chaotic attractor. In the case where the system is affected by a random noise, based on the stochastic sensitivity function, a description of the spread of random states around equilibrium and a chaotic attractor is given. A comparative analysis of the influence of parametric and additive noise on the attractors is carried out. Using the technique of confidence intervals, the probabilistic mechanisms of extinction of a population under the influence of noise are studied. Changes in the parametric boundaries of the existence of population under the influence of random disturbance are analyzed. In the third chapter the possible dynamic modes of the Lotka-Volterra model in determi\-nistic and stochastic cases are analyzed. Depending on the two parameters of the system, bifurcation diagram is constructed. Parametric zones of the existence of stable equilibria, cycles, closed invariant curves, and also chaotic attractors are studied. The bifurcations of the period doubling, Neimark--Sacker and the crisis are described. The complex shape of the basins of attraction is demonstrated. In addition to the deterministic system, the stochastic system is studied in detail, which describes the influence of external random disturbance. In the case of chaos, an algorithm for finding critical lines describing the boundary of a chaotic attractor is given. Based on the stochastic sensitivity function, confidence bands and ellipses are constructed to describe the spread of random states around a deterministic attractor.

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28

Capoco, Calvino Paulo. "Abordagens ao Modelo de Lotka-Volterra." Master's thesis, 2018. http://hdl.handle.net/10400.6/9962.

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Nesta dissertação, vamos considerar o modelo Lotka-Volterra. Este foi obtido na década 1920’s independentemente por Lotka e Volterra. O modelo é dado por um par de equações diferenciais não lineares de primeira ordem e considera a interação entre as duas populações. Existem três grandes tipos de interação: competição, cooperação e predador -presa. Neste trabalho, estudamos o modelo Lotka-Volterra com interação do tipo predador-presa. Para modelar a dinâmica entre as duas populações podemos adicionar termos ao modelo original de forma a torná-lo mais realista e sempre que possível estimar a sua estabilidade. No primeiro modelo a ser analisado, será introduzido um termo nas presas e será estudada sua estabilidade. Um dos termos a ser adicionado pode ser um controle, numa ou nas duas populações e pode ser visto como introdução ou remoção de elementos nas populações. No segundo e terceiro modelo, iremos introduzir um termo que deverá ser visto como um controle. Este será introduzido nos predadores e será do tipo ON-OFF. Em ambos os modelos iremos mostrar graficamente que os modelos aparentam convergir para um ponto numa zona específica. Todos serão modelados usando equações às diferenças mas para isso é necessário escolher um esquema numérico. Entre os mais comuns estão os métodos de Euler, Runge-Kutta e Mickens. Iremos usar o método de Mickens.
In this dissertation, we consider the Lotka-Volterra model. It was obtained in 1920’s independently by Lotka and Volterra. The model is given by two first-order nonlinear differential equations and consider the interaction between two populations. The three main types of interaction are competition, cooperation, and predator-prey. In this work, we study the Lotka-Volterra model of the predator-prey type. To model the dynamics between these two populations there can be added terms in an attempt to make it more realistic and if it is possible, to estimate its stability. In the first model, we add a term in the preys and its stability will be studied. One of the terms that can be added may be a control, in one or two populations and it can be seen as an introduction or removal of elements of the population or populations. In the second and third model, we will add a term that should be seen as a control. It will be added in the predators and will be an ON-OFF control. In these two last models, it will be shown graphically that the trajectories tend to converge to a point in a specific zone. All of them will be modeled by difference equations but, to do that, we need to choose some numerical scheme. The most common ones are Euler, Runge-Kutta and more recently Mickens method. We will use the Mickens Method.

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Li, Yu-Pan, and 李育磐. "Numerical Study of Lotka-Volterra Competition Models." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/83581527990761523269.

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碩士
國立交通大學
應用數學系所
101
In this thesis, we study the evolution of conditional dispersal using a Lotka-Volterra competition model for two competing species. We assume that two species are identical except for their dispersal strategies. Depending on the different parameter combinations, we determine that one of two possible behaviors can occur: coexistence, or extinction of one of the species. In this thesis, we find the parameter combinations which can lead the two species coexistence by numerical simulations. We try to Depict the distribution of the parameter combinations and discuss the distribution of the two species which change with time.

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Lin, Zih-yun, and 林子韻. "Dynamic Analysis of the Lotka-Volterra Competing Model." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/53500311875042631532.

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碩士
國立中正大學
數學所
97
In the Lotka-Volterra Competing Model of two species, we change the parameters after t1 second(s) so that the convergent conditions may be different from the case without turning point t1.

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Huang, Huang-cheng, and 黃皇程. "An enhanced application of Lotka–Volterra modelto forecast competing retail formats." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/pd9745.

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博士
國立交通大學
工業工程與管理系所
105
his research develops a sales forecasting model that can analyze the interaction effects of two retail competing formats (Convenience-oriented vs. Budget-oriented formats). A traditional approach to making such a forecast is based on the Lotka–Volterra equations (also called the LV-model). The LV-model assumes that the population of each species is affected by its self-growth, internal interaction within the species, and external interaction with other species. Most prior studies in business applications directly use sales data as input to the LV-model. The prior approach may result in misleading conclusions when sales data are embedded with seasonal variation, because this variation is not addressed in the original development of the LV-model. Therefore, this study proposes a forecasting framework (an enhanced application of the LV-model). The sales data of each retail format is considered as a compound data, which is decomposed into three individual components: (1) aggregate, (2) competition, and (3) seasonal components. The LV-model is used to forecast the competition component；the other two components are forecasted by typical time series methods；and the data of three components are finally combined into one. Empirical study indicates that the proposed method substantially outperforms the prior approach in terms of forecasting errors (4.4% vs.16.7% for Convenience-oriented and 5.8% vs. 16.2% for Budget-oriented). In addition, the proposed method reveals a more convincing predator-prey relationship between the two retail formats, which concludes that the Convenience-oriented is the predator. To the opposite, the prior approach, concluding that the Budget-oriented is the predator, is quite doubtful because the Convenience-oriented shall be preferred while the GDP grows over time. This research makes a contribution in how to appropriately apply the LV-model in forecasting revenue and analyzing the interaction effects of two competing business species. Keywords : Lotka–Volterra model ; Forecasting ; Retail formats

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"Persistence for "Kill the Winner" and Nested Infection Lotka-Volterra Models." Doctoral diss., 2016. http://hdl.handle.net/2286/R.I.40772.

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abstract: In recent decades, marine ecologists have conducted extensive field work and experiments to understand the interactions between bacteria and bacteriophage (phage) in marine environments. This dissertation provides a detailed rigorous framework for gaining deeper insight into these interactions. Specific features of the dissertation include the design of a new deterministic Lotka-Volterra model with n + 1 bacteria, n/n + 1 phage, with explicit nutrient, where the jth phage strain infects the first j bacterial strains, a perfectly nested infection network (NIN). This system is subject to trade-off conditions on the life-history traits of both bacteria and phage given in an earlier study Jover et al. (2013). Sufficient conditions are provided to show that a bacteria-phage community of arbitrary size with NIN can arise through the succession of permanent subcommunities, by the successive addition of one new population. Using uniform persistence theory, this entire community is shown to be permanent (uniformly persistent), meaning that all populations ultimately survive. It is shown that a modified version of the original NIN Lotka-Volterra model with implicit nutrient considered by Jover et al. (2013) is permanent. A new one-to-one infection network (OIN) is also considered where each bacterium is infected by only one phage, and that phage infects only that bacterium. This model does not use the trade-offs on phage infection range, and bacterium resistance to phage. The OIN model is shown to be permanent, and using Lyapunov function theory, coupled with LaSalle’s Invariance Principle, the unique coexistence equilibrium associated with the NIN is globally asymptotically stable provided that the inter- and intra-specific bacterial competition coefficients are equal across all bacteria. Finally, the OIN model is extended to a “Kill the Winner” (KtW) Lotka-Volterra model of marine communities consisting of bacteria, phage, and zooplankton. The zooplankton acts as a super bacteriophage, which infects all bacteria. This model is shown to be permanent.
Dissertation/Thesis
Doctoral Dissertation Applied Mathematics 2016

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Wu, Yun, and 吳勻. "Analyzing Apple and BlackBerry Smartphone Competition by the Lotka-Volterra Model." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/56s5tt.

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碩士
國立交通大學
管理學院管理科學學程
103
In last decade, with the rapid development of technology products, smartphones have gradually changed our lives. As a first-mover, BlackBerry introduced Push Mail service to the market by publishing the very first smartphone which is able to retrieve latest emails from the server autonomously. As a Late-comer, Apple launched their first smart phone shocked the market with its appearance, user interface, and other unique features. In this study, we employ Lotka-Volterra model to analyze the competitive operational relations between Apple and BlackBerry, in worldwide and North America smartphone markets. Also, we employ Bass model to estimate and predict and analyze which models, Lotka-Volterra model or Bass model, are more accurate. The estimation parameter result shows that in the world wide smartphone market, Apple and BlackBerry are in Predator-Prey relationship. But in North America smartphone market, these two companies are in the Amensalism relationship. The estimated results also indicate that, in the worldwide and North America markets, two companies will reach a stable equilibrium.

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Lin, Yu-Hsien, and 林育賢. "Analyzing Sales Revenues of Taiwan Airline Industry by the Lotka-Volterra Model." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/2564up.

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碩士
國立交通大學
管理學院管理科學學程
107
This study employs Lotka-Voltreea Model to investigate and development strategies for Aviation industry in Taiwan by comparing the dynamic competitive relation between China-Airline Corporation and EVA Air Corporation. This study applied to the accuracy of prediction for China Airline Corporation and EVA Air Corporation revenue trend with Lotka-Volterra Model. the result shows the relation between China-Airline Corporation and EVA Air Corporation is Commensalism, EVA Air Corporation monthy revenue benefits the revenue growth of China Airline Corporation, while China-Airline Corporation has no effect on EVA Air Corporation. The possible reason First, EVA Air Corporation emphasize flight safety, has won one of the safest airlines the world for consecutive six years, which has and it led China-Airline to grow together; Second, the success of EVA aerospace industrial strategy has stimulated China-Airline to follow the aerospace industry strategy of EVA Corporation. Our results also conclude that Lotka-Volterra model has excellent prediction ability and better fit on data samples than Bass model since the competitive and cooperative relation between China-Airline Corporation and EVA Air Corporation is considered in Lotka-Volterra model. In the equilibrium analysis, China Airline Corporation revenue will be convergent to NT$ 11,466 million per month, and EVA Air Corporation is NT$ 10,296 million per month. This result indicates that the relation between China-Airline Corporation and EVA Air Corporation will be stable in long-term competition.

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賴威民. "Analyzing Sales Revenues of Taiwan Tire Manufacturing Industry by the Lotka-Volterra Model." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/33p3r4.

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碩士
國立交通大學
管理學院管理科學學程
103
This study applies Lotka-Volterra Model to investigate the competition relation between two major tire manufacturers in Taiwan, Cheng Shin Rubber Ind. Co., Ltd. (CST), and Kenda Rubber Ind., Co., Ltd. (KENDA). By comparing the revenue performance and development strategies, the competitive and cooperative relation between CST and KENDA is verified and the equilibrium relation is predicted. Bass Model is employed in this study as well in order to evaluate the accuracy of prediction with Lotka-Volterra Model for the tire industry in Taiwan. The result shows that the revenue growth of CST benefits KENDA, however, KENDA has no influence on CST. The possible reason is that CST plays a pioneer in tire industry. CST aggrandized itself by investing overseas, including R&;D and product enhancement. Thus, CST established its brand awareness and customer confidence firstly. KENDA, as a follower, made less effort than CST. KENDA benefited from CST’s experience on layout arrangement and investment strategy and involved in emerging market with less cost on try and error or other barriers.In the equilibrium analysis, the revenue will be convergent to NTD$10,953,364,000 and NTD$2,698,975,000 for CST and KENDA. This result implies that in long-run, CST and KENDA will have stable equilibrium relation. The result also presents that Lotka-Volterra model has better prediction ability than Bass model.

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Chuang, Shih-Wen, and 莊仕文. "Analyzing Operational Revenues of Taiwanese Banks in China by the Lotka-Volterra Model." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/54444711762490260508.

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碩士
國立交通大學
管理科學系所
103
This study employs Lotka-Volterra model to analyze the competitive operational relations of Chinese branches between government-owned-banks and non-government-owned-banks. Two pairs of Lotka-Volterra equations are estimated in this work. One pair is the interest revenues of government-owned-banks and non-government-owned-banks. The other pair is the commission revenues of government-owned-banks and non-government-owned-banks from the Chinese branches of Taiwanese Banks. The estimation parameter result shows that the interest revenues from government-owned-banks will enhance those of non-government-owned-banks. This implies that the early entry of Taiwanese government-owned-banks into the mainland China. After government-owned-banks set up branches in China and offer loans to receive interest revenues, non-government-owned-banks follow government-owned-banks to set up branches in China and earn interest revenues. On the other hand, the results of parameter estimation show the commission revenues of government-owned-bank enhance the commission revenues of non-government-owned-bank, and vice versa. Regarding model’s forecast accuracy, the Lotka-Volterra model is more accurate than the Bass model in predicting interest revenues and commission revenues. In the long run, both the interest and commission revenues of government-owned-banks and non-government-owned-banks will reach a stable equilibrium. This study contributes to Taiwan’s and China’s governments the effective methods to measure the competition and cooperation in banking industry.

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Tsai, Yi-Fang, and 蔡宜芳. "Analysis of Competition and Cooperation in Taiwan Wafer Industry by Lotka-Volterra Model." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/9rds92.

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LIN, YAN-TING, and 林彥廷. "Numerical Simulation of Lotka-Volterra Reaction-Diffusion Advection Model for Two Competing Species." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/56735397692980597793.

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碩士
國立臺南大學
應用數學系碩士班
105
In this paper, we are using the finite difference methods to solve partial differential equation Lotka-Volterra reaction-diffusion advection model for two-competing species in R. First, We introduce the important parameters and significance of the model. Then, we use second order finite differences and discrete Fourier Transform to do the space discretization. Use Backward Euler method, Trapezoidal method and Runge-Kutta Method to do the time discretization and stability analysis.

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39

Hu, Tian Sheng, and 胡天生. "Analyzing Productivity Of Foreign Operator In Semiconductor Foundry By The Lotka-Volterra Model." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/96657163487754003282.

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碩士
國立交通大學
管理學院管理科學學程
103
This study is the first research productions and values of operators when introduceing the foreign operators in the IC foundry measurement area. Foreign operator is defined as the night shift foreign operator in the measurement area of IC foundry. Domestic operator is defined as the day shift non- foreign operator in the measurement area of IC foundry. We investigate whether the equilibrium relationship exists between foreign operator and domestic operator in the future. Introducing foreign operators will improve productions and values of operators at the same time.The mutual relation exists between foreign and domestic operators. Because foreign operators worried that their bad performance in Taiwan will force them to be repatriated, so they will be more actively work to achieve productions target . Domestic operators perform better afterwards. The empirical explains why introducing foreign operators can solve the shortage of operators.

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40

Yu-LunHuang and 黃于倫. "Lotka-Volterra Equation to Competitive Model with System Dynamics -The Case of Smartphone Operating System." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/3j4526.

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碩士
國立成功大學
經營管理碩士學位學程(AMBA)
101
In recent years, the network and technology products often brought people a refreshing surprise and made a great change in lifestyle, which became more convenient and abundant. The case of smart phone can explain the situation clearly. The Android and the iOS systems are the major operating systems of mobile phone, and the consideration of operation system is one of the reasons of purchasing smart phones. The market status of iOS and Android are closed-end and open-end respectively, which are shown in different competitive relationships. This study would like to discuss the key factors which may affect the competitive relationship in different stages. The Lotka-Volterra Model is based on the growth curve which is to discover the interaction between the two competitive species. And this article would like to utilize the Lotka-Volterra Model as a research framework and to discover the different competitive relationships. The ‘system dynamics’ is used as the research tool to build the competitive model of Lotka-Volterra. It is to analyze the impact of the two competitor’s sales and to simulate the sales. According to the simulation result which shows that the Lotka-Volterra competitive model holds a reasonable capability of simulation. Moreover, the parameter adjustment of Lotka-Volterra model provides the factors which affect the sales for both competitors. In addition, the growth rates of application of both sides are added in the Lotka-Volterra competitive model in order to simulate the sales for both sides. This article presents the results of simulation which may reveal the Volterra Model has a better simulation capability for smart phones market. Therefore, the Lotka-Volterra competitive model proposed in this study can be beneficial to the analysis of the competitive interaction relationship between two competitors.

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41

"A Lotka-Volterra model for multi-mode technological interaction : modeling competition, symbiosis and predator prey modes." International Center for Research on the Management of Technology, Sloan School of Management, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/2635.

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Carl W.I. Pistorius, James M. Utterback.
Cover title. "March 1996." "Technology Management in a Changing World, Proceedings of the Fifth International Conference on Management of Technology, Miami, Florida, February 27-March 1, 1996"--Added t.p.
Includes bibliographical references (leaves [7-8]).

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42

Chang, Ching-Yu, and 張景瑜. "The Application of Lotka-Volterra Model in the Analysis of Sales Revenues for Electronic Commerce Industry." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/c99bv6.

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43

Huang, Hsin-En, and 黃昕恩. "A Study on the patterns of word-of-mouth life cycle in Lotka-Volterra competition model." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/83296645578716331430.

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碩士
國立臺灣大學
統計碩士學位學程
104
Film industry plays an important role in global economic. Box office earnings increase year by year. In 2015, the United States box office earnings are about 10.1 billion dollars, with 38.3 billion dollars global box office earnings. We can found that film industry has a great potential, especially in the United States. As a result, our study will use the movies which are shown in the United States as research objects. Several researchers have studied the effect of amount of word-of-mouth in recent years, especially the electronic word-of-mouth. Although the effects of amount of word-of-mouth on film industry have been examined by many investigators, no studied have investigated the effect of the positive and negative commentary about movie. So this paper will discuss the effect of the positive and negative electronic commentary on movie. The purpose of this paper is to analyze the competitive relation between positive and negative commentary by Lotka-Volterra Model. Since different competitive relation will have different effects, this paper proposes Lotka-Volterra Model is good for analyzing the relation and intersection from both side.

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44

Chang, Chun-Hung, and 張俊鴻. "The Application of Lotka-Volterra Model in the Analysis of Sales Revenues for Taiwan’s Semiconductor Foundry Industry." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/43j42e.

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碩士
國立交通大學
管理學院管理科學學程
103
This study employs Lotka-Volterra Model to investigate the investment and development strategies for IC foundry industry in Taiwan by comparing the dynamic competitive relation between Taiwan Semiconductor Manufacturing Company (TSMC) and United Microelectronics Corporation (UMC). We explore whether TSMC and UMC compete or cooperate each other through analyzing TSMC’s and UMC’s monthly revenue. In addition, we conduct equilibrium analysis as well. This study also implements Bass Model to verify the accuracy of prediction for TSMC’s and UMC’s revenue trend with Lotka-Volterra Model. The result shows the relation between TSMC and UMC is Commensalism. UMC’s revenue growth benefits TSMC, while TSMC has no effect on UMC. The possible reason is that TSMC pursues the development of advanced technologies and improves capacity to fulfill customers’ demand. As a competitive follower, UMC triggers TSMC’s advancement, having the horse flies effect as proposed by Lincoln (1860) on TSMC. Our results also conclude that Lotka-Volterra model has better prediction ability and better fit on data samples than Bass model since the competitive and cooperative relation between TSMC and UMC is considered in Lotka-Volterra model. In the equilibrium analysis, under the circumstances of fully capacity utilization, production from different generations may have negative interaction among each other in TSMC. As a result, based on future self-competitive relation, TSMC’s revenue will be convergent to NT$ 74,185 million, and UMC is NT$ 13,105 million per month. This result tells the relation between TSMC and UMC will be stable equilibrium in long-term competition.

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Dai, Jia-Yuan, and 戴佳原. "The Effects of Diffusion and Advection on the Evolution of Competing Species: a Survey on the Lotka-Volterra Competition Model." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/58047753259105680129.

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碩士
臺灣大學
數學研究所
98
This thesis is a rather complete survey concerning an ecologically meaningful problem: how would two competing species evolve in a given spatially heterogeneous and isolated environment? A special kind of the Lotka-Volterra competition model is derived by assuming that the mechanisms of redistribution consist of mutual competition, random diffusion, and advective motion. The main task is to analyze the evolutionary results of the competing species in the long run, or equivalently, to determine the stability of equilibria of the model. The mathematical methods such as maximum principles, calculus of variation, and the theory of monotone dynamical systems are utilized as the standard procedure. The main conclusion is that both random diffusion and advective motion decide the evolutionary results; thus different combinations of diffusion rates and advective tendencies may influence the evolutionary results. Accordingly, a preliminary bifurcation diagram can be established to provide certain theoretically reliable predictions.

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46

Chia-YingWei and 魏佳瑩. "Using Lotka-Volterra and co-diffusion model to explore the interaction of two competitors: A study of fresh food industry." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/c3s7vv.

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碩士
國立成功大學
工業與資訊管理學系碩博士班
101
Convenience store is established in order to meet the life style of people nowadays. In Taiwan, the sprung up of convenience store shows that the important of the market. All the owners of convenience stores invest in the fresh food to share the market of fresh food. Above all, the definition of fresh food industry is concluded in this market. It reflects that the market of convenience stores is growing up. By quantitative research method, we suggest a specific data to clarify the competitive relationship between 7-ELEVEN and Family Mart. That is a visible proof rather than qualitative method. The Fresh food industry is now a new industry in Taiwan. We utilize the framework of innovation of diffusion theory to analyze the characteristic of fresh food industry. And then we apply co-diffusion model to find out whether the relation between them is complement or substitute. Above and beyond, we also utilize Lotka-Volterra model to find out the relationship. We discuss the cases with two different aspects, microcosmic and macroscopic, for a comprehensive investigation. As a result, we find that in co-diffusion model, there is a substitute relationship between Family Mart to 7-ELEVEN; on the contrary, there is a complement relationship between 7-ELEVEN and Family Mart. In Lotka-Volterra model, it shows that they are predator-prey. Therefore, in fresh food market, 7-ELEVEN really eats Family Mart but Family Mart also makes contribution. We give suggestions to different companies for their management.

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"Stoichiometric Producer-Grazer Models, Incorporating the Effects of Excess Food-Nutrient Content on Grazer Dynamics." Doctoral diss., 2014. http://hdl.handle.net/2286/R.I.25188.

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abstract: There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework that produce rich dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon, known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, needs to be incorporated into mathematical models. Here we present Lotka-Volterra type models to investigate the growth response of Daphnia to algae of varying P:C ratios. Using a nonsmooth system of two ordinary differential equations (ODEs), we formulate the first model to incorporate the phenomenon of the stoichiometric knife edge. We then extend this stoichiometric model by mechanistically deriving and tracking free P in the environment. This resulting full knife edge model is a nonsmooth system of three ODEs. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, leads to quantitatively different predictions than previous models that neglect to track free nutrients. The full model shows that the grazer population is sensitive to excess nutrient concentrations as a dynamical free nutrient pool induces extreme grazer population density changes. These modeling efforts provide insight on the effects of excess nutrient content on grazer dynamics and deepen our understanding of the effects of stoichiometry on the mechanisms governing population dynamics and the interactions between trophic levels.
Dissertation/Thesis
Ph.D. Applied Mathematics 2014

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Wong, Jessica. "Parameter Estimation for Nonlinear State Space Models." 2012. http://hdl.handle.net/10222/14741.

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This thesis explores the methodology of state, and in particular, parameter estimation for time series datasets. Various approaches are investigated that are suitable for nonlinear models and non-Gaussian observations using state space models. The methodologies are applied to a dataset consisting of the historical lynx and hare populations, typically modeled by the Lotka- Volterra equations. With this model and the observed dataset, particle filtering and parameter estimation methods are implemented as a way to better predict the state of the system. Methods for parameter estimation considered include: maximum likelihood estimation, state augmented particle filtering, multiple iterative filtering and particle Markov chain Monte Carlo (PMCMC) methods. The specific advantages and disadvantages for each technique are discussed. However, in most cases, PMCMC is the preferred parameter estimation solution. It has the advantage over other approaches in that it can well approximate any posterior distribution from which inference can be made.
Master's thesis

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