Bistability in a one-dimensional model of a two-predators-one-prey population dynamics system

Sergey Kryzhevich, Viktor Avrutin, Gunnar Söderbacka

Research output: Contribution to journalArticlepeer-review

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 onedimensional bimodal map. 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.
Original languageEnglish
Number of pages13
JournalLobachevskii Journal of Mathematics
StateE-pub ahead of print - 11 Sep 2021

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