TY - JOUR

T1 - Bistability in a one-dimensional model of a two-predators-one-prey population dynamics system

AU - Kryzhevich, Sergey

AU - Avrutin, Viktor

AU - Söderbacka, Gunnar

PY - 2021/9/11

Y1 - 2021/9/11

N2 - In this paper, we study a classical two-predators-one-prey model. The classicalmodel 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 mechanismthat leads to bistable regimes. Taking this mechanism into account, one can easily detectparameter regions where cycles with arbitrary high periods or chaotic attractors with arbitraryhigh numbers of bands coexist pairwise.

AB - In this paper, we study a classical two-predators-one-prey model. The classicalmodel 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 mechanismthat leads to bistable regimes. Taking this mechanism into account, one can easily detectparameter regions where cycles with arbitrary high periods or chaotic attractors with arbitraryhigh numbers of bands coexist pairwise.

UR - https://www.researchgate.net/publication/353941461_Bistability_in_a_one-dimensional_model_of_a_two-predators-one-prey_population_dynamics_system

M3 - Article

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

ER -