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Bistability in a One-Dimensional Model of a Two-Predators-One-Prey Population Dynamics System

Abstract

In this paper, we study a classical two-predators-one-prey model. The classical model described by a system of three ordinary differential equations can be reduced to a one-dimensional bimodalmap. We prove that this map has at most two stable periodic orbits. Besides, we describe the bifurcation structure of the map. Finally, we describe a mechanism that leads to bistable regimes. Taking this mechanism into account, one can easily detect parameter regions where cycles with arbitrary high periods or chaotic attractors with arbitrary high numbers of bands coexist pairwise.

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DOI:
Digital Object Identifier (open in new tab) 10.1134/S1995080222020135
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Copyright (2022 Pleiades Publishing, Ltd.)

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Category:
Articles
Type:
artykuły w czasopismach
Published in:
Lobachevskii Journal of Mathematics no. 42, pages 3486 - 3496,
ISSN: 1995-0802
Language:
English
Publication year:
2021
Bibliographic description:
Kryzhevich S., Avrutin V., Sӧderbacka G.: Bistability in a One-Dimensional Model of a Two-Predators-One-Prey Population Dynamics System// Lobachevskii Journal of Mathematics -Vol. 42,iss. 14 (2021), s.3486-3496
DOI:
Digital Object Identifier (open in new tab) 10.1134/s1995080222020135
Sources of funding:
  • COST_FREE
Verified by:
Gdańsk University of Technology

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