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

Sergey Kryzhevich; Viktor Avrutin; Gunnar Sӧderbacka

doi:10.1134/s1995080222020135

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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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

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