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Relevant bibliographies by topics / Lotka-Volterra theory

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Academic literature on the topic 'Lotka-Volterra theory'

Author: Grafiati

Published: 5 June 2025

Last updated: 15 July 2025

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Journal articles on the topic "Lotka-Volterra theory"

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Osei Fokuo, M., W. Obeng – Denteh, I. K. Dontwi, and P. A. A. Mensah. "Fixed point of discrete dynamical system of Lotka Volterra model." Scientia Africana 23, no. 4 (2024): 157–62. https://doi.org/10.4314/sa.v23i4.14.

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Fixed point theorem is one of the theories in mathematics that has make many proofs been in existence. Lotka-Volterra model is a widely used pair of first-order nonlinear differential equations used to interpret the dynamics of two species that is a predator and a prey. The paper employs the contraction mapping and the Banach Fixed point theory on the Discrete Dynamical type of the Lotka-Volterra to see the outcome of its behavior.The Banach Fixed Theoryis used in determining the fixed point of discrete dynamical system of Lotka Volterra model.The results shows that the solutions of Lotka Volt

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Wang, Yinuo, and Mingxia Lv. "Analysis for Digital Economy Ecosystem Based on Three-Dimensional Lotka-Volterra Model." Advances in Economics and Management Research 9, no. 1 (2024): 121. http://dx.doi.org/10.56028/aemr.9.1.121.2024.

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Inspired by the complex system theory, we have expanded the two-dimensional Lotka- Volterra model to three- dimensional Lotka-Volterra model to obtain the stability conditions for all the equilibrium points, and to analyze the symbiotic evolution among the central enterprises and other two sorts of satellite digital enterprises in the ecosystem of digital economy.

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Fernandez, Juan C. Gutierrez, and Claudia I. Garcia. "On Lotka–Volterra algebras." Journal of Algebra and Its Applications 18, no. 10 (2019): 1950187. http://dx.doi.org/10.1142/s0219498819501871.

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The purpose of this paper is to study the structure of Lotka–Volterra algebras, the set of their idempotent elements and their group of automorphisms. These algebras are defined through antisymmetric matrices and they emerge in connection with biological problems and Lotka–Volterra systems for the interactions of neighboring individuals.

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Xu, Changjin, Maoxin Liao, and Xiaofei He. "Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays." International Journal of Applied Mathematics and Computer Science 21, no. 1 (2011): 97–107. http://dx.doi.org/10.2478/v10006-011-0007-0.

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Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations

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Muhammadhaji, Ahmadjan, Rouzimaimaiti Mahemuti, and Zhidong Teng. "Periodic Solutions for n-Species Lotka-Volterra Competitive Systems with Pure Delays." Chinese Journal of Mathematics 2015 (September 14, 2015): 1–11. http://dx.doi.org/10.1155/2015/856959.

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We study a class of periodic general n-species competitive Lotka-Volterra systems with pure delays. Based on the continuation theorem of the coincidence degree theory and Lyapunov functional, some new sufficient conditions on the existence and global attractivity of positive periodic solutions for the n-species competitive Lotka-Volterra systems are established. As an application, we also examine some special cases of the system, which have been studied extensively in the literature.

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Mao, Shuhua, Mingyun Gao, and Min Zhu. "The impact of R&D on GDP study based on grey delay Lotka-Volterra model." Grey Systems: Theory and Application 5, no. 1 (2015): 74–88. http://dx.doi.org/10.1108/gs-11-2014-0042.

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Purpose – The purpose of this paper is to elevate the accuracy when predicting the gross domestic product (GDP) on research and development (R&D) and to develop the grey delay Lotka-Volterra model. Design/methodology/approach – Considering the lag effects between input in R&D and output in GDP, this paper estimated the delay value via grey delay relation analysis. Taking the delay into original Lotka-Volterra model and combining with the thought of grey theory and grey transform, the authors proposed grey delay Lotka-Volterra model, estimated the parameter of model and gave the discret

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Cui, Qingyi, Changjin Xu, Wei Ou, et al. "Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay." Mathematics 11, no. 23 (2023): 4808. http://dx.doi.org/10.3390/math11234808.

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All the time, differential dynamical models with delay has witness a tremendous application value in characterizing the internal law among diverse biological populations in biology. In the current article, on the basis of the previous publications, we formulate a new Lotka–Volterra commensal symbiosis system accompanying delay. Utilizing fixed point theorem, inequality tactics and an appropriate function, we gain the sufficient criteria on existence and uniqueness, non-negativeness and boundedness of the solution to the formulated delayed Lotka–Volterra commensal symbiosis system. Making use o

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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. Condition

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Balibrea, Francisco, Juan Luis García Guirao, Marek Lampart, and Jaume Llibre. "Dynamics of a Lotka–Volterra map." Fundamenta Mathematicae 191, no. 3 (2006): 265–79. http://dx.doi.org/10.4064/fm191-3-5.

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Ray, Tane S., Leo Moseley, and Naeem Jan. "A Predator–Prey Model with Genetics: Transition to a Self-Organized Critical State." International Journal of Modern Physics C 09, no. 05 (1998): 701–10. http://dx.doi.org/10.1142/s0129183198000601.

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A two species predator–prey model based on the Lotka–Volterra equations is proposed, where the fitness of an individual animal depends upon the relative strength of its genes. Simulations of the model show that the system passes from the standard oscillatory solution of the Lotka–Volterra equations into a steady-state regime, which exhibits many of the characteristics of self-organized criticality, including a 1/f power spectrum.

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Dissertations / Theses on the topic "Lotka-Volterra theory"

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Ramírez, Sadovski Valentín. "Qualitative theory of differential equations in the plane and in the space, with emphasis on the center-focus and on the Lotka-Volterra systems." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/669890.

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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, w

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Uechi, Risa. "Modeling of Biological and Economical Phenomena Based on Analysis of Nonlinear Competitive Systems." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199432.

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Aziz, Waleed. "Analytic and algebraic aspects of integrability for first order partial differential equations." Thesis, University of Plymouth, 2013. http://hdl.handle.net/10026.1/1468.

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This work is devoted to investigating the algebraic and analytic integrability of first order polynomial partial differential equations via an understanding of the well-developed area of local and global integrability of polynomial vector fields. In the view of characteristics method, the search of first integrals of the first order partial differential equations P(x,y,z)∂z(x,y) ∂x +Q(x,y,z)∂z(x,y) ∂y = R(x,y,z), (1) is equivalent to the search of first integrals of the system of the ordinary differential equations dx/dt= P(x,y,z), dy/dt= Q(x,y,z), dz/dt= R(x,y,z). (2) The trajectories of (2)

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Books on the topic "Lotka-Volterra theory"

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Voges, Jörg. Spieltheoretische Konzepte zur Untersuchung verallgemeinerter Lotka-Volterra-Systeme. S. Roderer, 1989.

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UNESCO. Working Group on Systems Analysis. Meeting. Lotka-Volterra-approach to cooperation and competition in dynamic systems: Proceedings of the 5th Meeting of UNESCO's Working Group on System Theory held on the Wartburg, Eisenach (GDR), March 5-9, 1984. Akademie-Verlag, 1985.

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UNESCO Working Group on System Theory. Meeting. Lotka-Volterra-Approach to Cooperation and Competition in Dynamic Systems: Proceedings of the 5th Meeting of UNESCO's Working Group on System Theory held on the Wartburg, Eisenach (GDR) March 5-9, 1984. Akademie-Verlag, 1985.

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4

Meeting of UNESCO's Working Group on System Theory (5th 1984 Eisenach, Germany). Lotka-Volterra-approach to cooperation and competition in dynamic systems: Proceedings of the 5th Meeting of UNESCO'S Working Group on System Theory held on the Wartburg, Eisenach (GDR) March 5-9, 1984. Akademie, 1985.

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5

UNESCO. Working Group on System Theory. Meeting. Lotka-Volterra-approach to cooperation and competitionin dynamic systems: Proceedings of the 5th Meeting of UNESCO'S Working Group on System Theory held on the Wartburg, Eisenach (GDR), March 5-9, 1984. Akademie-Verlag, 1985.

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6

Khailov, Evgenii, Nikolai Grigorenko, Ellina Grigorieva, and Anna Klimenkova. Controlled Lotka-Volterra systems in the modeling of biomedical processes. LCC MAKS Press, 2021. http://dx.doi.org/10.29003/m2448.978-5-317-06681-9.

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This book is devoted to a consistent presentation of the recent results obtained by the authors related to controlled systems created based on the Lotka-Volterra competition model, as well as to theoretical and numerical study of the corresponding optimal control problems. These controlled systems describe various modern methods of treating blood cancers, and the optimal control problems stated for such systems, reflect the search for the optimal treatment strategies. The main tool of the theoretical analysis used in this book is the Pontryagin maximum principle - a necessary condition for opt

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Figdor, Carrie. Cases. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198809524.003.0003.

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Chapter 3 introduces the use of mathematical models and modeling practices in contemporary biological and cognitive sciences. The familiar Lotka–Volterra model of predator–prey relations is used to explain these practices and show how they promote the extensions of predicates, including psychological predicates, into new and often unexpected domains. It presents two models of cognitive capacities that were developed to explain human behavioral data: Ratcliff’s drift-diffusion model of decision-making and Sutton and Barto’s temporal difference model of reinforcement learning. These are now used

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Book chapters on the topic "Lotka-Volterra theory"

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Yi, Zhang, and K. K. Tan. "Lotka-Volterra Recurrent Neural Networks with Delays." In Network Theory and Applications. Springer US, 2004. http://dx.doi.org/10.1007/978-1-4757-3819-3_5.

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Freguglia, Paolo, Eleonora Andreotti, and Armando Bazzani. "Modelling Ecological Systems from a Niche Theory to Lotka-Volterra Equations." In SEMA SIMAI Springer Series. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41120-6_1.

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Looijen, Rick C. "The Reduction of the Lotka/Volterra Competition Model to Modern Niche Theory." In Holism and Reductionism in Biology and Ecology. Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9560-5_10.

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Looijen, Rick C. "Erratum to: The Reduction of the Lotka/Volterra Competition Model to Modern Niche Theory." In Holism and Reductionism in Biology and Ecology. Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9560-5_14.

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Wilson, William G., and Justin P. Wright. "11 Community responses to environmental change: Results of Lotka-Volterra community theory." In Theoretical Ecology Series. Elsevier, 2007. http://dx.doi.org/10.1016/s1875-306x(07)80013-x.

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Doebeli, Michael. "Adaptive Diversification Due to Predator-Prey Interactions." In Adaptive Diversification (MPB-48). Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691128931.003.0005.

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This chapter discusses adaptive diversification due to predator–prey interactions. It has long been recognized that consumption, that is, predation, can not only exert strong selection pressure on the consumer, but also on the consumed species. However, predation has traditionally received much less attention than competition as a cause for the origin and maintenance of diversity. By using adaptive dynamics theory as well as individual-based models, the chapter then illustrates that adaptive diversification in prey species due to frequency-dependent predator–prey interactions is a theoretically plausible scenario. It also describes conditions for diversification due to predator–prey interactions in classical Lotka–Volterra models, which requires analysis of coevolutionary dynamics between two interacting species, and hence of adaptive dynamics in two-dimensional phenotype spaces.

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Abrams, Peter A. "The negativity, constancy, and continuity of competitive effects." In Competition Theory in Ecology. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780192895523.003.0006.

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Abstract This chapter uses relatively simple consumer–resource models to show that several phenomena that are impossible under the Lotka–Volterra model are common in models with resources. For the vast majority of models, all common measures of competitive effect differ depending on the size of the initial change used to make the measurement. Adding, removing, or changing the growth rate of a second consumer can produce, alter, or eliminate population cycles, and thereby alter the interaction. Changes in stability are almost always associated with large magnitude changes in competitive effects. If the experimental change used to measure the interspecific effect causes resource extinction, this often causes a discontinuous jump in the magnitude of the competitive effect. In two-resource systems, the possibility of resource extinction in the presence of a single consumer can lead to exclusion of a second consumer. In this case, the later arriving of two competitors always excludes the earlier one, producing a ‘posteriority’ effect. Such effects have never been observed. In systems where resource immigration prevents exclusion, posteriority does not occur. Systems in which each species has an exclusive resource are particularly likely to have very nonlinear competitive effects, and coexistence may be guaranteed in spite of high overlap in consumption rate curves.

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McCann, Kevin S. "A Primer for Dynamical Systems." In Food Webs (MPB-50). Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691134178.003.0002.

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This chapter introduces the reader to some of the main conceptual ideas behind dynamical systems theory from the perspective of an experimentalist. It first considers the qualitative approaches used to study complex problems before discussing dynamical systems and bifurcations. In particular, it examines the use of time series to represent solutions and dynamics in the phase space, phase space respresentations of equilibrium and nonequilibrium steady states, the qualitative analysis of steady states, and some of the mechanics of local stability analysis for an equilibrium using the Lotka–Volterra model for an equilibrium steady state. It also explores the relationship between the type of model dynamics and the geometry of the underlying mathematical functions. Finally, it presents an empirical example from ecology, Hopf bifurcation in an aquatic microcosm, to illustrate the main concepts of dynamical systems theory and shows that the mathematics of dynamical systems underlies the dynamics of real ecological systems.

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Chesson, Peter. "Species coexistence." In Theoretical Ecology. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198824282.003.0002.

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In most places on Earth, many similar species are found coexisting. This key observation is often explained in terms of ecological differences in how species interact with their shared environment, that is, in terms of their niche differences. Niche differences can to lead to stable coexistence in contrast to the ecological drift predicted by the neutral theory of community ecology. Coexistence becomes stabilized as density feedback within species is strengthened relative to density feedback between species. Coexistence is reflective of two distinct niche comparisons, niche overlap, and species relative average fitness. In general, low niche overlap (dissimilarity in use of the environment) and similar average fitnesses (similar average performance) favor coexistence. For a unified theory of species coexistence, it is shown how the Lotka–Volterra competition model can reflect and quantify several types of niche comparison, including comparisons of resource use, susceptibility to natural enemies, and temporal variation in activity.

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Allesina, Stefano, and Jacopo Grilli. "Models for large ecological communities—a random matrix approach." In Theoretical Ecology. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198824282.003.0006.

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Lotka and Volterra were among the first to attempt to mathematize the dynamics of interacting populations. While their work had a profound influence on ecology, leading to many of the results that were covered in the preceding chapters, their approach is difficult to generalize to the case of many interacting species. When the number of species in a community is sufficiently large, there is little hope of obtaining analytical results by carefully studying the system of dynamical equations describing their interactions. Here, we introduce an approach based on the theory of random matrices that exploits the very large number of species to derive cogent mathematical results. We review basic concepts in random matrix theory by illustrating their applications to the study of multispecies systems. We introduce tools that can be used to yield new insights into community ecology and conclude with a list of open problems.

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Conference papers on the topic "Lotka-Volterra theory"

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Rachmawati, Zahra Febrilia, Sutrima, and Ririn Setiyowati. "Cooperation analysis of automotive industry in Indonesia based on Lotka-Volterra model." In THE 4TH INTERNATIONAL CONFERENCE ON MATHEMATICS: EDUCATION, THEORY & APPLICATION (ICMETA) 2022. AIP Publishing, 2025. https://doi.org/10.1063/5.0262936.

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Bochuan Zheng and Zhang Yi. "Extracting long contour by using the competitive layer model of the Lotka-Volterra recurrent neural networks." In 2010 3rd International Conference on Advanced Computer Theory and Engineering (ICACTE 2010). IEEE, 2010. http://dx.doi.org/10.1109/icacte.2010.5579569.

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Nguyen-Van, Triet, and Noriyuki Hori. "A Discrete-Time Model for Lotka-Volterra Equations With Preserved Stability of Equilibria." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-63049.

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A Lotka-Volterra differential equation is discretized using a method proposed recently by the same authors for nonlinear autonomous systems and the stability of equilibrium points of the resulting discrete-time model is investigated. It is shown that when Jacobian matrix of the nonlinear equation is invertible, the equilibrium points of the model are identical to those of the original continuous-time system, and their asymptotic stability and instability are retained for any sampling period. While the method can be applied to any Lotka-Volterra types, simulation results are presented for a com

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Fradkov, Alexander, and Aleksandr Semenov. "Functional identification of the parameters multispecies Lotka-Volterra model." In 2022 6th Scientific School Dynamics of Complex Networks and their Applications (DCNA). IEEE, 2022. http://dx.doi.org/10.1109/dcna56428.2022.9923181.

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Semenov, Aleksandr, and Alexander Fradkov. "Parameters identification of the multispecies Lotka-Volterra model using discrete algorithm." In 2023 7th Scientific School Dynamics of Complex Networks and their Applications (DCNA). IEEE, 2023. http://dx.doi.org/10.1109/dcna59899.2023.10290695.

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Komninelli, Foteini, Athanasios Iliopoulos, and John G. Michopoulos. "Performance of a Lotka-Volterra System for Representing Biofouling Processes." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35002.

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In order to assess the feasibility and performance of a minimal multiphysics model for representing the spatiotemporal evolution of biofouling process, we selected the coupled diffusive generalization of the Lotka-Volterra PDEs to govern the spatiotemporal evolution of population densities of predator-prey colonies in a computational domain. The implementation of the finite element solution of the system was performed and the associated numerical solution of the system was achieved. An analysis was performed that highlights certain choices of the control parameters of the model and their effec

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Kim, Jeong Geun, Benedikt Haus, Brit-Maren Block, and Paolo Mercorelli. "An introductional lecture on chaotic systems through Lorenz attractor and forced Lotka Volterra equation for interdisciplinary education." In SEFI 50th Annual conference of The European Society for Engineering Education. Universitat Politècnica de Catalunya, 2022. http://dx.doi.org/10.5821/conference-9788412322262.1457.

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Is it possible to predict the future? How accurate is the prediction for the future? These questions are fascinating and intriguing ones in particular for young generations who look at their future with curiosity. For a long time, many have tried to quantitatively predict future behavior of systems more accurately with techniques such as time series analysis and derived dynamical models based on observed data. The paper proposes a lecture structure in which elements of chaos, which greatly impacts the predictive capabilities of dynamical models, are introduced through two classical examples of

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Reports on the topic "Lotka-Volterra theory"

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Gonzalez, Logan, Christopher Baker, Stacey Doherty, and Robyn Barbato. Ecological modeling of microbial community composition under variable temperatures. Engineer Research and Development Center (U.S.), 2024. http://dx.doi.org/10.21079/11681/48184.

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Soil microorganisms interact with one another within soil pores and respond to external conditions such as temperature. Data on microbial community composition and potential function are commonly generated in studies of soils. However, these data do not provide direct insight into the drivers of community composition and can be difficult to interpret outside the context of ecological theory. In this study, we explore the effect of abiotic environmental variation on microbial species diversity. Using a modified version of the Lotka-Volterra Competition Model with temperature-dependent growth ra

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Heinz, Kevin, Itamar Glazer, Moshe Coll, Amanda Chau, and Andrew Chow. Use of multiple biological control agents for control of western flower thrips. United States Department of Agriculture, 2004. http://dx.doi.org/10.32747/2004.7613875.bard.

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The western flower thrips (WFT), Frankliniella occidentalis (Pergande), is a serious widespread pest of vegetable and ornamental crops worldwide. Chemical control for Frankliniella occidentalis (Pergande) (Thysanoptera: Thripidae) on floriculture or vegetable crops can be difficult because this pest has developed resistance to many insecticides and also tends to hide within flowers, buds, and apical meristems. Predatory bugs, predatory mites, and entomopathogenic nematodes are commercially available in both the US and Israel for control of WFT. Predatory bugs, such as Orius species, can suppre

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