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

TL;DR

This paper analyzes a simplified one-dimensional model of a two-predators-one-prey system, revealing bistability, bifurcation structures, and conditions for complex dynamics like chaos and high-period cycles.

Contribution

It reduces the classical three-equation predator-prey model to a one-dimensional map and characterizes its stability and bifurcation behavior, highlighting the coexistence of multiple attractors.

Findings

The map has at most two stable periodic orbits.

Bifurcation structures allow for high-period cycles and chaos.

Parameter regions with coexisting attractors are identified.

Abstract

In this paper, we study the classical two-predators-one-prey model. The classical model described by a system of 3 ordinary differential equations can be reduced to a one-dimensional bimodal map. We prove that this map has at most two stable periodic orbits. Besides, we describe the structure of bifurcations of the map. 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.