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MODELING OF GLOBAL PROCESSES. NONLINEAR DYNAMICS AND HUMANITIES
Mathematical model of three competing populations and multistability of periodic regimes
B. H. Nguyen, V. G. Tsybulin Southern Federal University, Rostov-on-Don, Russia
Abstract:
Purpose of this work is to analyze oscillatory regimes in a system of nonlinear differential equations describing the competition of three non-antagonistic species in a spatially homogeneous domain. Methods. Using the theory of cosymmetry, we establish a connection between the destruction of a two-parameter family of equilibria and the emergence of a continuous family of periodic regimes. With the help of a computational experiment in MATLAB, a search for limit cycles and an analysis of multistability were carried out. Results. We studied dynamic scenarios for a system of three competing species for different coefficients of growth and interaction. For several combinations of parameters in a computational experiment, new continuous families of limit cycles (extreme multistability) are found. We establish bistability: the coexistence of isolated limit cycles, as well as a stationary solution and an oscillatory regime. Conclusion. We found two scenarios for locating a family of limit cycles regarding a plane passing through three equilibria corresponding to the existence of only one species. Besides cycles lying in this plane, a family is possible with cycles intersecting this plane at two points. We can consider this case as an example of periodic processes leading to overpopulation and a subsequent decline in numbers. These results will further serve as the basis for the analysis of systems of competing populations in spatially heterogeneous areas.
Keywords:
Volterra model, nonlinear differential equations, competition, family of limit cycles, multistability.
Received: 30.01.2023
Citation:
B. H. Nguyen, V. G. Tsybulin, “Mathematical model of three competing populations and multistability of periodic regimes”, Izvestiya VUZ. Applied Nonlinear Dynamics, 31:3 (2023), 316–333
Linking options:
https://www.mathnet.ru/eng/ivp534 https://www.mathnet.ru/eng/ivp/v31/i3/p316
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Abstract page: | 94 | Full-text PDF : | 43 | References: | 9 |
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