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In this paper, we study the classical two-predators-one-prey model. Theclassical model described by a system of 3 ordinary differential equations canbe reduced to a one-dimensional bimodal map. We prove that this map has at mosttwo stable periodic orbits. Besides, we describe the structure of bifurcationsof the map. Taking this mechanism into account, one can easily detect parameterregions where cycles with arbitrary high periods or chaotic attractors witharbitrary high numbers of bands coexist pairwise.

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