Model Map and Multistability for a Two Predator-One Prey System

Abstract

This work contains a review of some important results on a known two predators - one prey system. We also add essential new numerical results on multiple attractors. We consider the case when the predators coexist. We distinguish two possibilities. The first is when the dynamics is well described by the dynamics of a one dimensional map. We discuss the main behaviour of this map. For small parameter regions the map can have two attractors but no more than two. We give a numerical example, when these two attractors exist in the original three-dimensional model. The second case is when this model map is not working and something like spiral chaos often occurs. We give numerical results showing that in this case there can be at least four different attractors and discuss the behaviour of these.