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Journal articles on the topic 'Lotka-Volterra theory'

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Published: 5 June 2025

Last updated: 15 July 2025

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1

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 Volterra Model are the fixed points the of Model. Also, the outcome of contraction mapping and Banach fixed point theory shows that the fixed points serving as the limiting behavior of Lotka Volterra is continuous and convergent.

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2

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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3

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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4

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 for supporting the theoretical results are also included.

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5

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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6

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 discrete time analytic expression. Findings – Collecting the actual data of R&D and GDP in Wuhan China from 1995 until 2008, this paper figure out that the delay between R&D and GDP was 2.625 year and found the dealy time would would gradually be reduced with the economy increasing. Practical implications – Constructing the grey delay Lotka-Volterra model via above data, this paper shown that the precision was satisfactory when fitting the data of R&D and GDP. Comparing the forecasts with the actual data of GDP in Wuhan from 2009 until 2012, the error was small. Social implications – The result shows that R&D and GDP would be both growing fast in future. Wuhan will become a city full of activity. Originality/value – Considering the lag between R&D and GDP, this work estimated the delay value via a grey delay relation analysis and constructed a novel grey delay Lotka-Volterra model.

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7

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 of stability and bifurcation theory of delayed differential equation, we focus on the emergence of bifurcation behavior and stability nature of the formulated delayed Lotka–Volterra commensal symbiosis system. A new delay-independent stability and bifurcation conditions on the model are presented. By constructing a positive definite function, we explore the global stability. By constructing two diverse hybrid delayed feedback controllers, we can adjusted the domain of stability and time of appearance of Hopf bifurcation of the delayed Lotka–Volterra commensal symbiosis system. The effect of time delay on the domain of stability and time of appearance of Hopf bifurcation of the model is given. Matlab experiment diagrams are provided to sustain the acquired key outcomes.

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8

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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9

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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10

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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11

Ma, Li, and De Tang. "Existence and Stability of Stationary States of a Reaction–Diffusion-Advection Model for Two Competing Species." International Journal of Bifurcation and Chaos 30, no. 05 (2020): 2050065. http://dx.doi.org/10.1142/s0218127420500650.

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It is well known that the research of two species in the Lotka–Volterra competition system could create very interesting dynamics. In our paper, we investigate the global dynamical behavior of a classic Lotka–Volterra competition system by studying the steady states and corresponding stability by mainly employing the methods of monotone dynamical systems theory, Lyapunov–Schmidt reduction and spectral theory and so on. It illustrates that the dynamical behavior substantially relies on certain variable of the maximal growth rate. Furthermore, we obtain that one of the semi-trivial steady state solutions is a global attractor in some special cases. In biology, these results show that both of the species do not coexist and the mutant forces the extinction of resident species under some condition for two similar species system.

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12

Jiang, Yanan, Maoan Han, and Dongmei Xiao. "The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems." Scientific World Journal 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/705703.

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We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems inℝ3.

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13

Pekalski, Andrzej, and Dietrich Stauffer. "Three Species Lotka–Volterra Model." International Journal of Modern Physics C 09, no. 05 (1998): 777–83. http://dx.doi.org/10.1142/s0129183198000674.

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We present a model of a three-step food chain. Population A grows at a certain rate and at another rate is eaten by the population B which has its own birth rate but is, in turn, eaten at a different rate by the population C. The dynamics of the model is given by a set of differential equations and via Monte Carlo simulations. Our system undergoes sudden cataclysms in the form of partial destruction of one of the populations. We show that there exist threshold values for the possible percentage of destroyed populations, above which the system returns to its previous state, thus showing a self-regulatory character.

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14

Han, Maoan, Jaume Llibre, and Yun Tian. "On the Zero-Hopf Bifurcation of the Lotka–Volterra Systems in R 3." Mathematics 8, no. 7 (2020): 1137. http://dx.doi.org/10.3390/math8071137.

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Here we study 3-dimensional Lotka–Volterra systems. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there are some of these differential systems exhibiting at least six periodic orbits bifurcating from one of their equilibrium points. We remark that these systems with such six periodic orbits are non-competitive Lotka–Volterra systems. The proof is done using the algorithm that we provide for computing the periodic solutions that bifurcate from a zero-Hopf equilibrium based in the averaging theory of third order. This algorithm can be applied to any differential system having a zero-Hopf equilibrium.

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15

Kobayashi, Manami, Takashi Suzuki, and Yoshio Yamada. "Lotka-Volterra Systems with Periodic Orbits." Funkcialaj Ekvacioj 62, no. 1 (2019): 129–55. http://dx.doi.org/10.1619/fesi.62.129.

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16

Romero-Meléndez, Cutberto, David Castillo-Fernández, and Leopoldo González-Santos. "On the Boundedness of the Numerical Solutions’ Mean Value in a Stochastic Lotka–Volterra Model and the Turnpike Property." Complexity 2021 (October 22, 2021): 1–14. http://dx.doi.org/10.1155/2021/4445496.

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In this paper, we study some properties of the solutions of a stochastic Lotka–Volterra predator-prey model, namely, the boundedness in the mean of numerical solutions, the strong convergence for this kind of solutions, and the turnpike property of solutions of an optimal control problem in a population modelled by a Lotka–Volterra system with stochastic environmental fluctuations. Even though there are numerous results in the deterministic case, there are few results for the behavior of numerical solutions in a population dynamic with random fluctuations. First, we show, using the Euler–Maruyama scheme, that the boundedness of numerical solutions and the convergence of the scheme are preserved in the stochastic case. Second, we analyze a property of the long-term behavior of a Lotka–Volterra system with stochastic environmental fluctuations known as turnpike property. In optimal control theory, the optimal solutions dwell mostly in the neighborhood of a balanced equilibrium path, corresponding to the optimal steady-state solution. Our study shows, by means of the Stochastic Maximum Principle, that this turnpike property is preserved, when the noise in the system is small. Numerical simulations are implemented to support our results.

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17

Zhou, Houhua, Xu Cai, Junzhe Wang, and Fei Li. "Prediction and Conservation Recommendations for the Effects of Diversified Drought on Plant Community Species." Highlights in Science, Engineering and Technology 55 (July 9, 2023): 52–62. http://dx.doi.org/10.54097/hset.v55i.9917.

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Based on the analysis of plant community data and climate data, this paper established a plant community competition prediction model that includes weather and environmental factors by utilizing species competition theory and the Lotka-Volterra model. During the model construction process, the actual data was pre-processed and summarized for analysis, which ultimately determined the parameters of species quantity, growth rate, and precipitation, improving the accuracy and reliability of the model. Meanwhile, using the Lotka-Volterra model, a relationship model between biomass and time was established, and through the simulated annealing algorithm, two optimal species quantity changes were obtained. Finally, this paper optimized the multi-factor plant community Lotka-Volterra model through the genetic algorithm and obtained the optimal solution: the plant community can achieve the most beneficial competitive state with four species. This further proves the rationality and robustness of the model and also provides new methods and ideas for the management and protection of ecosystems. In summary, the results of this paper are of great significance for the stability and sustainable development of ecosystems and provide useful references for solving the problem of plant community competition and ecosystem stability.

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18

Huang, Dingxuan, Claudio O. Delang, and Yongjiao Wu. "An Improved Lotka–Volterra Model Using Quantum Game Theory." Mathematics 9, no. 18 (2021): 2217. http://dx.doi.org/10.3390/math9182217.

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Human decision-making does not conform to the independent decision-making hypothesis from classical decision-making theory. Thus, we introduce quantum decision-making theory into the Lotka–Volterra model (L–V model), to investigate player population dynamics while incorporating the initial strategy, game payoffs and interactive strategies in an open social system. Simulation results show that: (1) initial strategy, entanglement intensity of strategy interaction, and payoffs impact population dynamics; (2) In cooperative coexistence, game players mutually exceed the initial environmental capacity in an open system, but not in competitive coexistence; (3) In competitive coexistence, an initial strategy containing an entanglement intensity of strategies plays a vital role in game outcomes. Furthermore, our proposed model more realistically delineates the characteristics of population dynamics in competitive or cooperative coexistence scenarios.

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19

Wilson, W. G., P. Lundberg, D. P. Vazquez, et al. "Biodiversity and species interactions: extending Lotka-Volterra community theory." Ecology Letters 6, no. 10 (2003): 944–52. http://dx.doi.org/10.1046/j.1461-0248.2003.00521.x.

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20

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 (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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Brenig, L´eon. "Nonlinear dynamical systems seen through the scope of the Quasi-polynomial theory." e-Boletim da Física 5, no. 1 (2016): 1–13. http://dx.doi.org/10.26512/e-bfis.v5i1.9802.

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 A unified theory of nonlinear dynamical systems is presented. The unification relies on the Quasi-polynomial approach of these systems. The main result of this approach is that most nonlinear dynamical systems can be exactly transformed to a unique format, the Lotka-Volterra system. An abstract Lie algebraic structure underlying most nonlinear dynamical systems is found. This structure, based on two sets of operators obeying specific commutation rules and on a Hamiltonian expressed in terms of these operators, bears a strong similarity with the fundamental algebra of quantum physics. From these properties, two forms of the exact general solution can be constructed for all Lotka-Volterra systems. One of them corresponds to a Taylor series in power of time. In contrast with other Taylor series solutions methods for nonlinear dynamical systems, our approach provides the exact analytic form of the general coefficient of that series. The second form of the solution is given in terms of a path integral. These solutions can be transformed back to solutions of the general nonlinear dynamical systems.

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22

Jiang, Ye Yang, and Tian Fu Chai. "Time-Lag Lotka-Volterra System Application in Network Worm Modeling." Applied Mechanics and Materials 687-691 (November 2014): 2229–33. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.2229.

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This paper studies the impact of network time-lag on the spread of worms and virus, uses Lotka-Volterra equation theory with time delay, and studies the influence of network characteristics such as response time, predator copy size and interaction of network worms and predators.

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23

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 (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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24

Hu, Xiao Min, Hui Wang, and Zhi Xing Hu. "Data Processing in Biological Behavior Analysis of a Delayed Impulsive Lotka-Volterra Model with Mutual Interference." Advanced Materials Research 1046 (October 2014): 396–402. http://dx.doi.org/10.4028/www.scientific.net/amr.1046.396.

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A delayed impulsive Lotka-Volterra model with mutual interference was established. With the help of Mawhin’s Continuation Theorem in coincidence degree theory, a sufficient condition is found for the existence of positive periodic solutions of the system. A numerical simulation is given to illustrate main results.

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25

Xu, Changjin, and Yusen Wu. "Dynamics in a Lotka-Volterra Predator-Prey Model with Time-Varying Delays." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/956703.

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A Lotka-Volterra predator-prey model with time-varying delays is investigated. By using the differential inequality theory, some sufficient conditions which ensure the permanence and global asymptotic stability of the system are established. The paper ends with some interesting numerical simulations that illustrate our analytical predictions.

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Niyaz, Tursuneli, and Ahmadjan Muhammadhaji. "Positive Periodic Solutions of Cooperative Systems with Delays and Feedback Controls." International Journal of Differential Equations 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/502963.

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This paper studies a class of periodicnspecies cooperative Lotka-Volterra systems with continuous time delays and feedback controls. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin, some new sufficient conditions on the existence of positive periodic solutions are established.

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Li, Yongkun, and Kaihong Zhao. "2 N POSITIVE PERIODIC SOLUTIONS TO N SPECIES NON‐AUTONOMOUS LOTKA‐VOLTERRA UNIDIRECTIONAL FOOD CHAINS WITH HARVESTING TERMS." Mathematical Modelling and Analysis 15, no. 3 (2010): 313–26. http://dx.doi.org/10.3846/1392-6292.2010.15.313-326.

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By using the Mawhin continuation theorem of coincidence degree theory and some results on inequalities, we establish the existence of 2 n positive periodic solutions for n species non‐autonomous Lotka‐Volterra unidirectional food chains with harvesting terms. Two examples are given to illustrate the effectiveness of our results.

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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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Muhammadhaji, Ahmadjan, and Zhidong Teng. "Global Attractivity of a Periodic DelayedN-Species Model of Facultative Mutualism." Discrete Dynamics in Nature and Society 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/580185.

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Two classes of periodicN-species Lotka-Volterra facultative mutualism systems with distributed delays are discussed. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin and the Lyapunov function method, some new sufficient conditions on the existence and global attractivity of positive periodic solutions are established.

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Su, Rina, and Chunrui Zhang. "Stability and Hopf bifurcation periodic orbits in delay coupled Lotka-Volterra ring system." Open Mathematics 17, no. 1 (2019): 962–78. http://dx.doi.org/10.1515/math-2019-0074.

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Abstract In this paper, we consider a class of delay coupled Lotka-Volterra ring systems. Based on the symmetric bifurcation theory of delay differential equations and representation theory of standard dihedral groups, properties of phase locked periodic solutions are given. Moreover, the direction and the stability of the Hopf bifurcation periodic orbits are obtained by using normal form and center manifold theory. Finally, the research results are verified by numerical simulation.

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Zhao, Kaihong, Liang Ding, and Fengzao Yang. "Multiple Periodic Solutions to a Kind of Lotka-Volterra Food-Chain System with Delays and Impulses on Time Scales." ISRN Applied Mathematics 2012 (December 30, 2012): 1–29. http://dx.doi.org/10.5402/2012/769267.

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By using Mawhin’s continuation theorem of coincidence degree theory and some skills of inequalities, we establish the existence of at least 2n periodic solutions for a kind of n-species Lotka-Volterra food-chain system with delays and impulses on time scales. One example is given to illustrate the effectiveness of our results.

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32

Constantin, Bendrea, and Stan Adrian. "Delay differential systems. A generalization of the Lotka-Volterra model." Annals of the ”Dunarea de Jos” University of Galati. Fascicle II, Mathematics, Physics, Theoretical Mechanics 47, no. 2 (2024): 46–49. https://doi.org/10.35219/ann-ugal-math-phys-mec.2024.2.02.

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The first mathematical laws used in the theory of survival were introduced by Th. Malthus (1798-Principle of population; 1803-The theory of population), B. Gompertz (1860), and W. Makeham (1874). They proposed different exponential laws to describe the intensity of death, which then formed the basis for the biometric functions of survival. In the twentieth century, the development of demographic research, as well as the study of various epidemics affecting populations, led to the emergence and evolution of new methods for solving problems in survival theory. Lotka-Volterra (in their Predator-Prey model) described the differential equations of population growth (in humans, microorganisms, and other species). These models were later improved by E. M. Wright and P. J. Wangersky (1978), who more plausibly assumed that the phenomena of immigration-emigration could represent the biological reaction of self-regulation of a population, and that this factor acts with a certain delay. The use of random processes and, later, stochastic differential equations contributed to the evolution and diversification of mathematical models in biological systems. In this article, we have developed a variational functional framework for the description of problems associated with delayed differential systems. We have thus made a generalization of the Lotka-Volterra model.

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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 (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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34

Zhao, Kaihong. "Existence of Almost-Periodic Solutions for Lotka-Volterra Cooperative Systems with Time Delay." Journal of Applied Mathematics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/270104.

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This paper considers the existence of positive almost-periodic solutions for almost-periodic Lotka-Volterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.

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Maličký, Peter. "Interior periodic points of a Lotka–Volterra map." Journal of Difference Equations and Applications 18, no. 4 (2012): 553–67. http://dx.doi.org/10.1080/10236198.2011.583241.

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Minic, Djordje, and Sinisa Pajevic. "Emergent “quantum” theory in complex adaptive systems." Modern Physics Letters B 30, no. 11 (2016): 1650201. http://dx.doi.org/10.1142/s0217984916502018.

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Motivated by the question of stability, in this paper we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka–Volterra dynamics, the relevant effective “Planck constant” associated with such emergent “quantum” theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently nonclassical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.

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LI, YONGKUN, and KAIHONG ZHAO. "MULTIPLE POSITIVE PERIODIC SOLUTIONS TO m-LAYER PERIODIC LOTKA–VOLTERRA NETWORK-LIKE MULTIDIRECTIONAL FOOD-CHAIN WITH HARVESTING TERMS." Analysis and Applications 09, no. 01 (2011): 71–96. http://dx.doi.org/10.1142/s0219530511001741.

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An m-layer peiodic Lotka–Volterra network-like multidirectional food-chain with harvesting terms is proposed in this paper. By applying Mawhin's continuation theorem of coincidence degree theory and some skills of the inequalities, sufficient conditions which guarantee the existence of [Formula: see text] positive periodic solutions of the system are obtained. An example is given to illustrate the effectiveness of our results.

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Fang, Lini, N'gbo N'gbo, and Yonghui Xia. "Almost periodic solutions of a discrete Lotka-Volterra model via exponential dichotomy theory." AIMS Mathematics 7, no. 3 (2022): 3788–801. http://dx.doi.org/10.3934/math.2022210.

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<abstract><p>In this paper, we consider a discrete non-autonomous Lotka-Volterra model. Under some assumptions, we prove the existence of positive almost periodic solutions. Our analysis relies on the exponential dichotomy for the difference equations and the Banach fixed point theorem. Furthermore, by constructing a Lyapunov function, the exponential convergence is proved. Finally, a numerical example illustrates the effectiveness of the results.</p></abstract>

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Chen, Shanshan, Junping Shi, Zhisheng Shuai, and Yixiang Wu. "Global dynamics of a Lotka–Volterra competition patch model*." Nonlinearity 35, no. 2 (2021): 817–42. http://dx.doi.org/10.1088/1361-6544/ac3c2e.

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Abstract The global dynamics of the two-species Lotka–Volterra competition patch model with asymmetric dispersal is classified under the assumptions that the competition is weak and the weighted digraph of the connection matrix is strongly connected and cycle-balanced. We show that in the long time, either the competition exclusion holds that one species becomes extinct, or the two species reach a coexistence equilibrium, and the outcome of the competition is determined by the strength of the inter-specific competition and the dispersal rates. Our main techniques in the proofs follow the theory of monotone dynamical systems and a graph-theoretic approach based on the tree-cycle identity.

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Zeng, X. Y., B. Shi, and M. J. Gai. "A discrete periodic lotka-volterra system with delays." Computers & Mathematics with Applications 47, no. 4-5 (2004): 491–500. http://dx.doi.org/10.1016/s0898-1221(04)90040-5.

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Zhang, Wei, and Jasmine Siu Lee Lam. "Maritime cluster evolution based on symbiosis theory and Lotka–Volterra model." Maritime Policy & Management 40, no. 2 (2013): 161–76. http://dx.doi.org/10.1080/03088839.2012.757375.

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SAMANTA, G. P., A. Mondal, D. Sahoo, and P. Dolai. "A prey-predator system with herd behaviour of prey in a rapidly fluctuating environment." Mathematics in Applied Sciences and Engineering 1, no. 1 (2019): 16–26. http://dx.doi.org/10.5206/mase/8196.

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A statistical theory of non-equilibrium fluctuation in damped Volterra-Lotka prey-predator system where prey population lives in herd in a rapidly fluctuating random environment has been presented. The method is based on the technique of perturbation approximation of non-linear coupled stochastic differential equations. The characteristic of group-living of prey population has been emphasized using square root of prey density in the functional response.

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Zhang, Mengqing, Jing Tian, and Keyue Zou. "Asymptotic stability of a stochastic age-structured cooperative Lotka-Volterra system with Poisson jumps." Electronic Journal of Differential Equations 2023 (2023): 1–18. http://dx.doi.org/10.58997/ejde.2023.02.

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In this article, we study a stochastic age-structured cooperative Lotka-Volterra system with Poisson jumps. Applying the M-matrix theory, we prove the existence and uniqueness of a global solution for the system. Then we use an optimized Euler-Maruyama numerical scheme to approximate the solution. We obtain second-moment boundedness and convergence rate of the numerical solutions. The numerical solutions illustrate the theoretical results.

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BAISHYA, M., and C. CHAKRABORTI. "Non-equilibrium fluctuation in volterra-lotka systems." Bulletin of Mathematical Biology 49, no. 1 (1987): 125–31. http://dx.doi.org/10.1016/s0092-8240(87)80037-x.

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Baishya, M. C., and C. G. Chakraborti. "Non-equilibrium fluctuation in Volterra-Lotka systems." Bulletin of Mathematical Biology 49, no. 1 (1987): 125–31. http://dx.doi.org/10.1007/bf02459962.

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Xu, Changjin. "Delay-Induced Oscillations in a Competitor-Competitor-Mutualist Lotka-Volterra Model." Complexity 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/2578043.

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This paper deals with a competitor-competitor-mutualist Lotka-Volterra model. A series of sufficient criteria guaranteeing the stability and the occurrence of Hopf bifurcation for the model are obtained. Several concrete formulae determine the properties of bifurcating periodic solutions by applying the normal form theory and the center manifold principle. Computer simulations are given to support the theoretical predictions. At last, biological meaning and a conclusion are presented.

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ZHAO, KAIHONG, LIANG DING, and FENGZAO YANG. "EXISTENCE OF MULTIPLE PERIODIC SOLUTIONS TO LOTKA–VOLTERRA NETWORK-LIKE FOOD-CHAIN SYSTEM WITH DELAYS AND IMPULSES ON TIME SCALES." International Journal of Biomathematics 07, no. 01 (2014): 1450003. http://dx.doi.org/10.1142/s179352451450003x.

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In this paper, we have studied a general kind of n-species Lotka–Volterra network-like food-chain system with delays and impulses on time scales. Applying Mawhin's continuation theorem of coincidence degree theory and some skills of inequalities, some sufficient criteria have been established to guarantee the existence of at least 2n periodic solutions to this model. One example is given to illustrate the effectiveness of our results.

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Zhang, Hui, Feng Feng, Bin Jing, and Yingqi Li. "Almost Periodic Solution of a Multispecies Discrete Mutualism System with Feedback Controls." Discrete Dynamics in Nature and Society 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/268378.

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We consider an almost periodic multispecies discrete Lotka-Volterra mutualism system with feedback controls. We firstly obtain the permanence of the system by utilizing the theory of difference equation. By means of constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique positive almost periodic solution which is uniformly asymptotically stable. An example together with numerical simulation indicates the feasibility of the main result.

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Matsutani, Shigeki. "p-adic difference-difference Lotka-Volterra equation and ultra-discrete limit." International Journal of Mathematics and Mathematical Sciences 27, no. 4 (2001): 251–60. http://dx.doi.org/10.1155/s0161171201010808.

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We study the difference-difference Lotka-Volterra equations inp-adic number space and itsp-adic valuation version. We point out that the structure of the space given by taking the ultra-discrete limit is the same as that of thep-adic valuation space. Since ultra-discrete limit can be regarded as a classical limit of a quantum object, it implies that a correspondence between classical and quantum objects might be associated with valuation theory.

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Israel, Giorgio. "The Emergence of Biomathematics and the Case of Population Dynamics A Revival of Mechanical Reductionism and Darwinism." Science in Context 6, no. 2 (1993): 469–509. http://dx.doi.org/10.1017/s0269889700001484.

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The ArgumentThe development of modern mathematical biology took place in the 1920s in three main directions: population dynamics, population genetics, and mathematical theory of epidemics. This paper focuses on the first trend which is considered the most significant. Modern mathematical theory of population dynamics is characterized by three aspects (the first two being in a somewhat critical relationship): the emergence of the mathematical modeling approach, the attempt at establishing it in a reductionist-mechanist conceptual framework, and the revival of Darwinism. The first section is devoted to the analysis of the concept of mathematical model and the second one presents an example of a mathematical model (Van der Pol's model of heartbeat) which is a good prototype of that concept. In section 3 the main trends of mathematization of biology and the cultural and scientific contexts in which they found their development are discussed. Sections 4 and 5 are devoted to the contributions of V. Volterra and A. J. Lotka, to the analysis of the differences of their scientific conceptions, and to a discussion of a case study: the priority dispute concerning the discovery of the Volterra-Lotka equations. The historical analysis developed in this paper is also intended to detect the roots of some recent trends of mathematization of biology.

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