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Journal articles on the topic 'MODELO DE LOTKA-VOLTERRA'

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Published: 4 June 2021

Last updated: 14 February 2022

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1

Segarra, Jaime. "MÉTODOS NUMÉRICOS RUNGE-KUTTA Y ADAMS BASHFORTH-MOULTON EN MATHEMATICA." Revista Ingeniería, Matemáticas y Ciencias de la Información 7, no. 14 (July 15, 2020): 13–32. http://dx.doi.org/10.21017/rimci.2020.v7.n14.a81.

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n este estudio, el objetivo principal es realizar el análisis de los métodos numéricos Runge-Kutta y Adams Bashforth-Moulton. Para cumplir con el objetivo se utilizó el sistema de ecuaciones diferenciales del modelo Lotka-Volterra y se usó el software matemático Wolfram Mathematica. En los resultados se realiza la comparación de los métodos RK4, AB4 y AM4 con el comando NDSolve utilizando el modelo Lotka-Volterra. Los resultados obtenidos en los diagramas de fase y la tabla de puntos de la iteración indicaron que el método RK4 tiene mayor precisión que los métodos AB4 y AM4.

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2

Amaya Cedrón, Luis Andrés. "Modelo de Lotka - Volterra en la biomatemática Solución de sistema depredador-presa." Ciencias 4, no. 4 (December 28, 2020): 99–110. http://dx.doi.org/10.33326/27066320.2020.4.991.

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En la investigación, el modelo presa-depredador, también conocido como el modelo Lotka-Volterra, ha sido un punto de partida para el desarrollo de nuevas técnicas y teorías matemáticas. El modelo presadepredador se ocupa de la interacción entre dos especies, donde una de ellas (presa) tiene abundante comida y la segunda especie (depredador) tiene suministro de alimentos exclusivamente a la población de presas. Donde se supone también que, durante el proceso, en un intervalo de tiempo t, el medio no debería cambiar favoreciendo a ninguna de las especies y que cualquier adaptación genética es lo suficientemente lenta (Figueiredo, 2014). En este trabajo haremos el análisis de problema clásico de Presa-depredador.

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3

Noronha, Viviane De Lima, and Rosana Da Paz Ferreira. "ESTUDO DE UM MODELO MATEMÁTICO APLICADO AO CONTROLE BIOLÓGICO DA Ceratitis capitata (WIEDEMANN) (DIPTERA: TEPHRITIDAE) PELO Diachasmimorpha longicaudata (ASHMEAD) (HYMENOPTERA: BRACONIDAE) NA FRUTICULTURA BRASILEIRA." Revista Eletrônica Perspectivas da Ciência e Tecnologia - ISSN: 1984-5693 9, Único (November 8, 2017): 2. http://dx.doi.org/10.22407/1984-5693.2017.v9.p.2-25.

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Os maiores prejuízos causados à fruticultura pelas moscas-das-frutas estão relacionados aos problemas fitossanitários, que vão desde a queda precoce dos frutos até a sua desqualificação para a indústria e consumo in natura. Métodos que visam minimizar os prejuízos econômicos e que são concomitantemente viáveis ao meio-ambiente e eficazes no combate às moscas-das-frutas, como por exemplo, o controle biológico que ocorre através de inundações de parasitoides, como o Diachasmimorpha longicaudata, vêm sendo estudados e estimulados. Existem diversos modelos matemáticos que simulam a dinâmica entre espécies. Dentre esses modelos destacamos o de Lokta-Volterra clássico, que também é conhecido como o modelo "presa-predador". Mediante ao exposto, este trabalho teve como objetivo estudar um modelo matemático do tipo Lotka-Volterra aplicado ao controle biológico da mosca-das-frutas Ceratitis capitata pelo Diachasmimorpha longicaudata e a fruticultura nacional; partindo de uma sobre os principais dados biológicos e ecológicos dessas espécies, informações essas essenciais para a formulação do modelo proposto. A metodologia da pesquisa foi composta por duas etapas que consistiram em coleta de dados e definição de variáveis, como primeira parte e, montagem, plotagem e validação do modelo, como segunda parte da metodologia.

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4

Montaño Arias, Noé Manuel, and Juan Manuel Sánchez-Yañez. "Nitrification in tropical soils linked to microbial competition: a model based on Lotka-Volterra theory." Ecosistemas 23, no. 3 (December 23, 2014): 98–104. http://dx.doi.org/10.7818/ecos.2014.23-3.13.

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5

Da Silva, Welber Faustino, and Orlando Dos Santos Pereira. "Análise quantitativa do crescimento populacional da cidade de Seropédica-RJ sob a influência dos estudantes da Universidade Federal Rural do Rio de Janeiro." Revista Eletrônica TECCEN 9, no. 1 (October 3, 2016): 03. http://dx.doi.org/10.21727/teccen.v9i1.204.

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Neste trabalho pretendeu-se analisar o quanto os estudantes da Universidade Federal Rural do Rio de Janeiro (UFRRJ), que são moradores da cidade de Seropédica, influenciam quantitativamente e economicamente no crescimento da população local, uma vez que a UFRRJ tem sua sede localizada nas proximidades da cidade de Seropédica. Para isso, foi aplicado um modelo de crescimento definido por um sistema de equações diferenciais, devido a Lotka-Volterra, que envolve a iteração entre duas espécies, neste caso a população da cidade e apopulação de estudantes, sabendo que o número de moradias desocupadas é dependente da procura pelos estudantes para aluguéis e estas moradias ocupadas influenciam também a oferta e a construção de novos empreendimentos na cidade.

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Da Silva, Welber Faustino, and Orlando Dos Santos Pereira. "Análise Quantitativa do Crescimento Populacional da Cidade de Seropédica-RJ sob a Influência dos Estudantes da Universidade Federal Rural do Rio de Janeiro." Revista Eletrônica TECCEN 9, no. 1 (June 30, 2016): 03. http://dx.doi.org/10.21727/teccen.v9i1.782.

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Neste trabalho pretendeu-se analisar o quanto os estudantes da Universidade Federal Rural do Rio de Janeiro (UFRRJ), que são moradores da cidade de Seropédica, influenciam quantitativamente e economicamente no crescimento da população local, uma vez que a UFRRJ tem sua sede localizada nas proximidades da cidade de Seropédica. Para isso, foi aplicado um modelo de crescimento definido por um sistema de equações diferenciais, devido a Lotka-Volterra, que envolve a iteração entre duas espécies, neste caso a população da cidade e apopulação de estudantes, sabendo que o número de moradias desocupadas é dependente da procura pelos estudantes para aluguéis e estas moradias ocupadas influenciam também a oferta e a construção de novos empreendimentos na cidade.

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7

Salazar-Villegas, Alejandro, Viviana Morillo-López, Álvaro Morales-Aramburo, and Marco Márquez-Godoy. "Evaluación de la dinámica de población de bacterias magnetotácticas (MTBs) en medios naturales y enriquecidos, comparación con resultados teóricos obtenidos a partir del modelo de competencia de Lotka-Volterra." Respuestas 14, no. 1 (May 5, 2016): 40–49. http://dx.doi.org/10.22463/0122820x.524.

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Todas las MTBs reportadas hasta la fecha, han compartido la propiedad de ser muy difíciles de cultivar. Sin embargo, las características particulares de los nanocristales magnéticos (comúnmente de magnetita o greigita) que crecen en el interior de estos microorganismos, hace que sea muy interesante la búsqueda de estrategias que permitan obtener grandes cantidades de estas partículas. En este trabajo se presenta un método para aumentar la tasa de crecimiento de MTBs provenientes del embalse de La Fe, Colombia, enriqueciendo su medio natural con una solución de vitaminas, una solución de minerales y quinato férrico como fuente de hierro. Además, se utiliza el modelo de competencia de Lotka-Volterra para identificar posibles factores que sean determinantes en la interacción de las MTBs con su entorno biótico. Para esto se consideran las MTBs como una especie y los microorganismos no-magnetotácticos como la especie rival. Los resultados sugieren una curva de crecimiento con dos etapas diferenciables. Una etapa inicial que puede considerarse como la fase lag, toma alrededor de 25 días, y una etapa de crecimiento poblacional (fase Log) con un máximo en el día 60. Es posible que esta técnica de enriquecimiento aumente hasta 6.1 veces la población de MTBs naturales. El nivel de correlación entre los resultados teóricos y los experimentales es significativo. Esto sugiere que hay factores de competencia entre las MTBs y los microorganismos no-magnetotácticos de su ambiente natural, que influyen de manera importante en su dinámica de población. Se requieren otros estudios para confirmar esta hipótesis.Palabras Clave: Magnetotactic bacteria (MTB); Population dynamic; Enrichment; Competitive factors; Bacteria culture

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8

LIAN, BAOSHENG, and SHIGENG HU. "STOCHASTIC DELAY GILPIN–AYALA COMPETITION MODELS." Stochastics and Dynamics 06, no. 04 (December 2006): 561–76. http://dx.doi.org/10.1142/s0219493706001888.

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In this paper, we investigate a stochastic Gilpin–Ayala competition system, which is more general and more realistic than the classical Lotka–Volterra competition system. We reveal that the environmental noise will not only suppress a potential population explosion in the stochastic delay Gilpin–Ayala competition system but also make the solutions stochastically ultimately bounded. Comparing the classical Lotka–Volterra with Gilpin–Ayala competition system, we find that the latter has better proprieties.

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9

Nurrohman, Reza Kusuma, Ardiansyah Ardiansyah, and Bayu Dwi Apri Nugroho. "Lotka Volterra Model Simulation for Rice-field Rat and Tyto Alba Owls in Sumpiuh District, Banyumas Regency, Central Java." agriTECH 39, no. 4 (November 5, 2019): 323. http://dx.doi.org/10.22146/agritech.46456.

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Rice-field rat (Rattus argentiventer) is a rodent that has a high level of productivity. These animals attack rice plants from the vegetative to the generative phase. This research aimed to analyze and to predict the accuracy of the use of owls with mathematical equations model in Kebokura and Lebeng villages, Sumpiuh district. Lotka - Volterra and Competitive Lotka-Volterra models were used to predict the population dynamics of Owl (predator) and rice-field rats (prey), then Runge - Kutta numerical method was applied to analyze the population dynamics of predator and prey at a certain time. The results of the analyses using the Lotka – Volterra, Competitive Lotka - Volterra equations and simulation data, each graph data showed that the rats’ population was able to be maximally suppressed. Based on the analysis result, started with 24 owls and 1,689 rats, the rats’ population could be suppressed to 104 using Lotka – Volterra, and to 176 using the Competitive Lotka – Volterra model. Then in the first and second simulation, started with 50 and 100 owls and 1,689 rats, analysis using Lotka – Volterra and Competitive Lotka – Volterra showed that the rat population could be suppressed to as much as 126, 188 and 145, 189, respectively. Based on the analysis, it could be concluded that use of Serak Jawa owl strategy was able to reduce and stabilize the rat populations. Furthermore, the higher population of owls can prevent the population explosion of rats and can suppress the rat population to a lower number.

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10

KLOEDEN, P. E., and C. PÖTZSCHE. "DYNAMICS OF MODIFIED PREDATOR-PREY MODELS." International Journal of Bifurcation and Chaos 20, no. 09 (September 2010): 2657–69. http://dx.doi.org/10.1142/s0218127410027271.

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Besides being structurally unstable, the Lotka–Volterra predator-prey model has another shortcoming due to the invalidity of the principle of mass action when the populations are very small. This leads to extremely large populations recovering from unrealistically small ones. The effects of linear modifications to structurally unstable continuous-time predator-prey models in a (small) neighbourhood of the origin are investigated here. In particular, it is shown that typically either a global attractor or repeller arises depending on the choice of coefficients.The analysis is based on Poincaré mappings, which allow an explicit representation for the classical Lotka–Volterra equations.

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11

Tuladhar, Rohisha, Fidel Santamaria, and Ivanka Stamova. "Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior." Entropy 22, no. 9 (August 31, 2020): 970. http://dx.doi.org/10.3390/e22090970.

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We present a biological fractional n-species delayed cooperation model of Lotka-Volterra type. The considered fractional derivatives are in the Caputo sense. Impulsive control strategies are applied for several stability properties of the states, namely Mittag-Leffler stability, practical stability and stability with respect to sets. The proposed results extend the existing stability results for integer-order n−species delayed Lotka-Volterra cooperation models to the fractional-order case under impulsive control.

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12

Fu, Xiaoxia, Ping Zhang, and Juzhi Zhang. "Forecasting and Analyzing Internet Users of China with Lotka–Volterra Model." Asia-Pacific Journal of Operational Research 34, no. 01 (February 2017): 1740006. http://dx.doi.org/10.1142/s0217595917400061.

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In the background of big data era, the ability to accurately forecast the number of the Internet users has considerable implications for evaluating the growing trend of a newly-developed business. In this paper, we use four models, the Gompertz model, the Logistic model, the Bass model, and the Lotka–Volterra model, to forecast the Internet population in China with the historical data during 2007 to 2014. We compare the prediction accuracy of the four models using the criterions such as the mean absolute percentage error (MAPE), the mean absolute error (MAE) and the root mean square error (RMSE). We find that the Lotka–Volterra model has the highest prediction accuracy. Moreover, we use the Lotka–Volterra model to investigate the relationship between the rural Internet users and the urban Internet users in China. The estimation results show that the relationship is commensalism.

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13

MUKHAMEDOV, FARRUKH, and MANSOOR SABUROV. "ON DISCRETE LOTKA-VOLTERRA TYPE MODELS." International Journal of Modern Physics: Conference Series 09 (January 2012): 341–46. http://dx.doi.org/10.1142/s2010194512005405.

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The Lotka-Volterra (in short LV) model is a second order nonlinear differential equation frequently used to describe the dynamics of biological systems in which two groups of species, predators and their preys interact. One of the basic results of the LV model is that under suitable conditions the LV model can exhibit any asymptotical behavior such as equilibrium states, periodic cycles, and attractors. The discrete analogy of LV model has been considered by many researchers and has been called a quadratic LV model. In a discrete case, one of the unexpected results is that a quadratic LV model cannot exhibit a periodic cycle. In this paper we study nonlinear LV type models which include quadratic LV as a particular case. Unlike quadratic LV models, LV type models can exhibit any asymptotical behavior such as equilibrium states, periodic cycles, and attractors.

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14

Alves, Michele O., Marcos T. O. Pimenta, and Antonio Suárez. "Lotka–Volterra models with fractional diffusion." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, no. 3 (March 16, 2017): 505–28. http://dx.doi.org/10.1017/s0308210516000305.

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We study Lotka–Volterra models with fractional Laplacian. To do this we study in detail the logistic problem and show that the sub–supersolution method works for both the scalar problem and for systems. We apply this method to show the existence and non-existence of positive solutions in terms of the system parameters.

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15

Schimming, Rainer. "Conservation laws for Lotka-Volterra models." Mathematical Methods in the Applied Sciences 26, no. 17 (2003): 1517–28. http://dx.doi.org/10.1002/mma.431.

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16

Antonov, Andrey, Svetoslav Nenov2, and Tzvetelin Tzvetkov. "PREY-PREDATOR TRIDIAGONAL LOTKA-VOLTERRA MODELS." INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS AND APPLICATIONS 17, no. 1 (2018): 45–59. http://dx.doi.org/10.12732/ijdea.v17i1.5727.

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17

Ramadan, Baleanu, and Nassar. "Highly Accurate Numerical Technique for Population Models via Rational Chebyshev Collocation Method." Mathematics 7, no. 10 (October 1, 2019): 913. http://dx.doi.org/10.3390/math7100913.

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The present work introduces the application of rational Chebyshev collocation technique for approximating bio-mathematical problems of continuous population models for single and interacting species (C.P.M.). We study systematically the logistic growth model in a population, prey-predator model: Lotka-Volterra system (L.V.M.), the simple two-species Lotka-Volterra competition model (L.V.C.M.) and the prey-predator model with limit cycle periodic behavior (P.P.M.). For testing the accuracy, the numerical results for our method and others existing methods as well as the exact solution are compared. The obtained numerical results indicate the ability, the reliability and the accuracy of the present method.

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18

Wang, Qi, Jingyue Yang, and Feng Yu. "Global well-posedness of advective Lotka–Volterra competition systems with nonlinear diffusion." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 5 (April 3, 2019): 2322–48. http://dx.doi.org/10.1017/prm.2019.10.

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AbstractThis paper investigates the global well-posedness of a class of reaction–advection–diffusion models with nonlinear diffusion and Lotka–Volterra dynamics. We prove the existence and uniform boundedness of the global-in-time solutions to the fully parabolic systems under certain growth conditions on the diffusion and sensitivity functions. Global existence and uniform boundedness of the corresponding parabolic–elliptic system are also obtained. Our results suggest that attraction (positive taxis) inhibits blowups in Lotka–Volterra competition systems.

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19

Wilson, Alan. "Boltzmann, Lotka and Volterra and spatial structural evolution: an integrated methodology for some dynamical systems." Journal of The Royal Society Interface 5, no. 25 (December 11, 2007): 865–71. http://dx.doi.org/10.1098/rsif.2007.1288.

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It is shown that Boltzmann's methods from statistical physics can be applied to a much wider range of systems, and in a variety of disciplines, than has been commonly recognized. A similar argument can be applied to the ecological models of Lotka and Volterra. Furthermore, it is shown that the two methodologies can be applied in combination to generate the Boltzmann, Lotka and Volterra (BLV) models. These techniques enable both spatial interaction and spatial structural evolution to be modelled, and it is argued that they potentially provide a much richer modelling methodology than that currently used in the analysis of ‘scale-free’ networks.

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20

Cronström, Christofer, and Milan Noga. "Multi-Hamiltonian structure of Lotka-Volterra and quantum Volterra models." Nuclear Physics B 445, no. 2-3 (July 1995): 501–15. http://dx.doi.org/10.1016/0550-3213(95)00152-i.

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21

LAHAM, MOHAMED FARIS, ISTHRINAYAGY KRISHNARAJAH, and ABDUL KADIR JUMAAT. "A NUMERICAL STUDY ON PREDATOR PREY MODEL." International Journal of Modern Physics: Conference Series 09 (January 2012): 347–53. http://dx.doi.org/10.1142/s2010194512005417.

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Stochastic spatial models are becoming a popular tool for understand the ecological and evolution of ecosystem problems. We consider the predator prey interactions in term of stochastic representation of this Lotka-Volterra model and explore the use of stochastic processes to extinction behavior of the interacting populations. Here, we present simulation of stochastic processes of continuous time Lotka-Volterra model. Euler method has been used to solve the predator prey system. The trajectory spiral graph has been plotted based on obtained solution to show the population cycle of predator as a function of time.

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22

Spencer, Matthew, and Jason E. Tanner. "LOTKA-VOLTERRA COMPETITION MODELS FOR SESSILE ORGANISMS." Ecology 89, no. 4 (April 2008): 1134–43. http://dx.doi.org/10.1890/07-0941.1.

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23

Hu, Yangzi, Fuke Wu, and Chengming Huang. "Stochastic Lotka–Volterra models with multiple delays." Journal of Mathematical Analysis and Applications 375, no. 1 (March 2011): 42–57. http://dx.doi.org/10.1016/j.jmaa.2010.08.017.

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24

Richmond, Peter, and Lorenzo Sabatelli. "Peer pressure and Generalised Lotka Volterra models." Physica A: Statistical Mechanics and its Applications 344, no. 1-2 (December 2004): 344–48. http://dx.doi.org/10.1016/j.physa.2004.06.148.

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Marasco, A., A. Picucci, and A. Romano. "Market share dynamics using Lotka–Volterra models." Technological Forecasting and Social Change 105 (April 2016): 49–62. http://dx.doi.org/10.1016/j.techfore.2016.01.017.

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26

Gutiérrez, R., and M. J. Rosales. "Diffusion approximations for lotka – volterra type models." Communications in Statistics. Stochastic Models 14, no. 4 (January 1998): 809–32. http://dx.doi.org/10.1080/15326349808807502.

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27

Bakhanova, Yulia V., Alexey O. Kazakov, and Alexander G. Korotkov. "Spiral chaos in Lotka-Volterra like models." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 19, no. 2 (June 29, 2017): 13–24. http://dx.doi.org/10.15507/2079-6900.19.201701.013-024.

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Abu‐Rqayiq, Abdullah, and Ernest Barany. "Singularity of Lotka‐Volterra models under unfoldings." Mathematical Methods in the Applied Sciences 42, no. 6 (January 17, 2019): 1759–71. http://dx.doi.org/10.1002/mma.5470.

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Gutiérrez, R., and M. J. Rosales. "Diffusion approximations for lotka - volterra type models." Communications in Statistics - Theory and Methods 14, no. 4 (1998): 809–32. http://dx.doi.org/10.1080/03610929808828950.

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30

Vadillo, Fernando. "Comparing stochastic Lotka–Volterra predator-prey models." Applied Mathematics and Computation 360 (November 2019): 181–89. http://dx.doi.org/10.1016/j.amc.2019.05.002.

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López-Gómez, Julián, and Marcela Molina-Meyer. "Superlinear indefinite systems: Beyond Lotka–Volterra models." Journal of Differential Equations 221, no. 2 (February 2006): 343–411. http://dx.doi.org/10.1016/j.jde.2005.05.009.

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32

Ramadan, M. A., and M. A. Abd El Salam. "Spectral collocation method for solving continuous population models for single and interacting species by means of exponential Chebyshev approximation." International Journal of Biomathematics 11, no. 08 (November 2018): 1850109. http://dx.doi.org/10.1142/s1793524518501097.

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In this paper, an efficient and accurate method is presented to solve continuous population models for single and interacting species using spectral collocation method with exponential Chebyshev (EC) functions. The first problem is a logistic growth model in a population, while the second problem is a prey–predator model: Lotka–Volterra system, the third is a simple 2-species Lotka–Volterra competition model, and the final one is a prey–predator model with limit cycle periodic behavior. The high accuracy of this method is verified through some numerical examples. The obtained numerical results are compared with other methods, showing that the proposed method gives higher accuracy.

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33

Staňková, Kateřina, Alessandro Abate, Maurice W. Sabelis, Ján Buša, and Li You. "Joining or opting out of a Lotka–Volterra game between predators and prey: does the best strategy depend on modelling energy lost and gained?" Interface Focus 3, no. 6 (December 6, 2013): 20130034. http://dx.doi.org/10.1098/rsfs.2013.0034.

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Apart from interacting, prey and predators may also avoid each other by moving into refuges where they lack food, yet survive by switching to an energy-saving physiological state. Lotka–Volterra models of predator–prey interactions ignore this option. Therefore, we have modelled this game of ‘joining versus opting out’ by extending Lotka–Volterra models to include portions of populations not in interaction and with different energy dynamics. Given this setting, the prey's decisions to join or to opt out influence those of the predator and vice versa, causing the set of possible strategies to be complex and large. However, using game theory, we analysed and published two models showing (i) which strategies are best for the prey population given the predator's strategy, and (ii) which are best for prey and predator populations simultaneously. The predicted best strategies appear to match empirical observations on plant-inhabiting predator and prey mites. Here, we consider a plausible third model that does not take energy dynamics into account, but appears to yield contrasting predictions. This supports our assumption to extend Lotka–Volterra models with ‘interaction-dependent’ energy dynamics, but more work is required to prove that it is essential and that what is best for the population is also best for the individual.

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Cantrell, Robert Stephen. "Global higher bifurcations in coupled systems of nonlinear eigenvalue problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 106, no. 1-2 (1987): 113–20. http://dx.doi.org/10.1017/s0308210500018242.

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SynopsisCoexistent steady-state solutions to a Lotka–Volterra model for two freely-dispersing competing species have been shown by several authors to arise as global secondary bifurcation phenomena. In this paper we establish conditions for the existence of global higher dimensional n-ary bifurcation in general systems of multiparameter nonlinear eigenvalue problems which preserve the coupling structure of diffusive steady-state Lotka–Volterra models. In establishing our result, we mainly employ the recently-developed multidimensional global multiparameter theory of Alexander–Antman. Conditions for ternary steady-state bifurcation in the three species diffusive competition model are given as an application of the result.

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35

Singh, Abhyudai. "Stochastic dynamics of predator-prey interactions." PLOS ONE 16, no. 8 (August 12, 2021): e0255880. http://dx.doi.org/10.1371/journal.pone.0255880.

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The interaction between a consumer (such as, a predator or a parasitoid) and a resource (such as, a prey or a host) forms an integral motif in ecological food webs, and has been modeled since the early 20th century starting from the seminal work of Lotka and Volterra. While the Lotka-Volterra predator-prey model predicts a neutrally stable equilibrium with oscillating population densities, a density-dependent predator attack rate is known to stabilize the equilibrium. Here, we consider a stochastic formulation of the Lotka-Volterra model where the prey’s reproduction rate is a random process, and the predator’s attack rate depends on both the prey and predator population densities. Analysis shows that increasing the sensitivity of the attack rate to the prey density attenuates the magnitude of stochastic fluctuations in the population densities. In contrast, these fluctuations vary non-monotonically with the sensitivity of the attack rate to the predator density with an optimal level of sensitivity minimizing the magnitude of fluctuations. Interestingly, our systematic study of the predator-prey correlations reveals distinct signatures depending on the form of the density-dependent attack rate. In summary, stochastic dynamics of nonlinear Lotka-Volterra models can be harnessed to infer density-dependent mechanisms regulating predator-prey interactions. Moreover, these mechanisms can have contrasting consequences on population density fluctuations, with predator-dependent attack rates amplifying stochasticity, while prey-dependent attack rates countering to buffer fluctuations.

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Kunwar, Laxman Bahadur. "Analyzing Predator-Prey Model." Mathematics Education Forum Chitwan 4, no. 4 (November 15, 2019): 79–87. http://dx.doi.org/10.3126/mefc.v4i4.26361.

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In this article, we consider a system involving two-species living in the same environment and describe the model for their population growth presented by Lotka and Volterra. The model is the foundation for the development of many other models. The model is known as Predator-Prey Model or Lotka-Volterra system. In more modern theories, there will be multiple species each with their own interactions but we will limit ourselves to this simpler but highly instructive classical system. We shall cover various standard tools for analysing such systems. We shall discuss dynamic solutions, equilibrium solutions and phase curves that best illustrate the phenomena.

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Solomon, Sorin. "Generalized Lotka-Volterra (GLV) Models of Stock Markets." Advances in Complex Systems 03, no. 01n04 (January 2000): 301–22. http://dx.doi.org/10.1142/s0219525900000224.

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The Generalized Lotka-Volterra (GLV) model: [Formula: see text] provides a general method to simulate, analyze and understand a wide class of phenomena that are characterized by power-law probability distributions: [Formula: see text] and truncated Levy flights fluctuations [Formula: see text]. We show how the model applies to economic systems.

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Munteanu, Florian. "A study of a three-dimensional competitive Lotka–Volterra system." ITM Web of Conferences 34 (2020): 03010. http://dx.doi.org/10.1051/itmconf/20203403010.

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In this paper we will consider a community of three mutually competing species modeled by the Lotka–Volterra system: $$ {\left\{ {\dot x} \right._i} = {x_i}\left( {{b_i} - \sum\limits_{i = 1}^3 {{a_{ij}}{x_j}} } \right),i = 1,2,3 $$ where xi(t) is the population size of the i-th species at time t, Ẋi denote $${{dxi} \over {dt}}$$ and aij, bi are all strictly positive real numbers. This system of ordinary diﬀerential equations represent a class of Kolmogorov systems. This kind of systems is widely used in the mathematical models for the dynamics of population, like predator-prey models or diﬀerent models for the spread of diseases. A qualitative analysis of this Lotka-Volterra system based on dynamical systems theory will be performed, by studying the local behavior in equilibrium points and obtaining local dynamics properties.

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Morrison, Rebecca E. "Data-Driven Corrections of Partial Lotka–Volterra Models." Entropy 22, no. 11 (November 18, 2020): 1313. http://dx.doi.org/10.3390/e22111313.

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In many applications of interacting systems, we are only interested in the dynamic behavior of a subset of all possible active species. For example, this is true in combustion models (many transient chemical species are not of interest in a given reaction) and in epidemiological models (only certain subpopulations are consequential). Thus, it is common to use greatly reduced or partial models in which only the interactions among the species of interest are known. In this work, we explore the use of an embedded, sparse, and data-driven discrepancy operator to augment these partial interaction models. Preliminary results show that the model error caused by severe reductions—e.g., elimination of hundreds of terms—can be captured with sparse operators, built with only a small fraction of that number. The operator is embedded within the differential equations of the model, which allows the action of the operator to be interpretable. Moreover, it is constrained by available physical information and calibrated over many scenarios. These qualities of the discrepancy model—interpretability, physical consistency, and robustness to different scenarios—are intended to support reliable predictions under extrapolative conditions.

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TAKEUCHI, Y. "Diffusion effect on stability of Lotka-Volterra models." Bulletin of Mathematical Biology 48, no. 5-6 (1986): 585–601. http://dx.doi.org/10.1016/s0092-8240(86)90009-1.

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Svirezhev, Yuri. "Lotka–Volterra models and the global vegetation pattern." Ecological Modelling 135, no. 2-3 (December 2000): 135–46. http://dx.doi.org/10.1016/s0304-3800(00)00355-0.

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Avelino, P. P., D. Bazeia, J. Menezes, and B. F. de Oliveira. "String networks in ZN Lotka–Volterra competition models." Physics Letters A 378, no. 4 (January 2014): 393–97. http://dx.doi.org/10.1016/j.physleta.2013.11.041.

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Satulovsky, Javier E. "Lattice Lotka–Volterra Models and Negative Cross-diffusion." Journal of Theoretical Biology 183, no. 4 (December 1996): 381–89. http://dx.doi.org/10.1006/jtbi.1996.0229.

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Hovsepian, Karen, Peter Anselmo, and Subhasish Mazumdar. "Supervised inductive learning with Lotka–Volterra derived models." Knowledge and Information Systems 26, no. 2 (January 16, 2010): 195–223. http://dx.doi.org/10.1007/s10115-009-0280-5.

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López-Gómez, Julián, and Rosa Pardo San Gil. "Coexistence regions in Lotka-Volterra models with diffusion." Nonlinear Analysis: Theory, Methods & Applications 19, no. 1 (July 1992): 11–28. http://dx.doi.org/10.1016/0362-546x(92)90027-c.

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Takeuchi, Yasuhiro. "Diffusion effect on stability of Lotka-Volterra models." Bulletin of Mathematical Biology 48, no. 5-6 (September 1986): 585–601. http://dx.doi.org/10.1007/bf02462325.

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Remien, Christopher H., Mariah J. Eckwright, and Benjamin J. Ridenhour. "Structural identifiability of the generalized Lotka–Volterra model for microbiome studies." Royal Society Open Science 8, no. 7 (July 2021): 201378. http://dx.doi.org/10.1098/rsos.201378.

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Population dynamic models can be used in conjunction with time series of species abundances to infer interactions. Understanding microbial interactions is a prerequisite for numerous goals in microbiome research, including predicting how populations change over time, determining how manipulations of microbiomes affect dynamics and designing synthetic microbiomes to perform tasks. As such, there is great interest in adapting population dynamic theory for microbial systems. Despite the appeal, numerous hurdles exist. One hurdle is that the data commonly obtained from DNA sequencing yield estimates of relative abundances, while population dynamic models such as the generalized Lotka–Volterra model track absolute abundances or densities. It is not clear whether relative abundance data alone can be used to infer parameters of population dynamic models such as the Lotka–Volterra model. We used structural identifiability analyses to determine the extent to which a time series of relative abundances can be used to parametrize the generalized Lotka–Volterra model. We found that only with absolute abundance data to accompany relative abundance estimates from sequencing can all parameters be uniquely identified. However, relative abundance data alone do contain information on relative interaction strengths, which is sufficient for many studies where the goal is to estimate key interactions and their effects on dynamics. Using synthetic data of a simple community for which we know the underlying structure, local practical identifiability analysis showed that modest amounts of both process and measurement error do not fundamentally affect these identifiability properties.

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Wang, Zheng-Xin, and Hong-Tao Zhu. "Testing the trade relationships between China, Singapore, Malaysia and Thailand using grey Lotka-Volterra competition model." Kybernetes 45, no. 6 (June 6, 2016): 931–45. http://dx.doi.org/10.1108/k-04-2015-0110.

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Purpose – Since the construction of China-ASEAN Free Trade Area (CAFTA) launched in 2002, the bilateral trade increased rapidly. The purpose of this paper is to test the competition and cooperation in trade relationships between China and the main trading partners (Singapore, Malaysia and Thailand (SMT)) from ASEAN in international trade under CAFTA. Design/methodology/approach – Grey Lotka-Volterra competition models are established for testing the trade relationships between China and SMT, respectively, based on the data of import and export from 2003 to 2014. To improve modeling accuracy, the interpolated coefficients for dynamic background value are introduced into the grey Lotka-Volterra model. The optimal parameters are solved through minimizing the mean absolute percentage error and the constraint of parameter relationships. Besides, eigenvalues of the Jacobian matrix are adopted to carry out the stability of equilibrium points of the trade relationships. Findings – As the beneficiary party, China has mutual benefit and win-win trade relationship with Singapore, while it has predator-prey trade relationships with Malaysia and Thailand. The future exports from SMT to China will stabilize at 462.31, 598.13 and 447.03 billion dollars, respectively. The future exports from China to SMT will stabilize at 637.16, 943.71 and 827.52 billion dollars, respectively. Practical implications – This study can be regarded as an important reference for China and its trading partners from ASEAN. The modeling results can help the decision makers to formulate appropriate international trade strategies to gain and maintain competitive advantages. Originality/value – A new approach to testing the trade relationships is proposed based on grey Lotka-Volterra competition model. The study also proposed a dynamic optimization method for the background value of grey Lotka-Volterra model.

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ZHANG, YU, ZHIDONG TENG, and SHUJING GAO. "A NEW RESULT ON THE PERIODIC SOLUTIONS FOR DISCRETE PERIODIC n-SPECIES COMPETITION MODELS WITH DELAYS." International Journal of Biomathematics 02, no. 03 (September 2009): 253–66. http://dx.doi.org/10.1142/s1793524509000650.

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A discrete time periodic n-species Lotka–Volterra type competitive model with delays is investigated. By using Gaines and Mawhin's continuation theorem based on the coincidence degree theory, a new sufficient condition on the existence of positive periodic solutions of the model is established.

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ABBO, Bakari, BAGAYOGO Moussa, MINOUNGOU Youssouf, and Youssouf PARE. "Comparative Numerical Study of SBA (Somé Blaise-Abbo) Method and Homotopy Perturbation Method (HPM) on Biomathematical Models Type Lotka-Volterra." Journal of Mathematics Research 13, no. 3 (April 14, 2021): 22. http://dx.doi.org/10.5539/jmr.v13n3p22.

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In this work the Homotopy Perturbation Method (HPM) is used to find an exact or approximate solutions of Lotka-Volterra models. Then we compare the HPM solution with the solution given by SBA (Somé Blaise Abbo) method.

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