Coexistence of attractors in a model for two predators

We consider an ODE-model for n predators feeding on the same prey. We mainly consider the case n = 2 and we give conditions and discuss different types for coexistence of the predators. For such a system there are no equilibrium at which the predators coexist. Anyhow they can coexist in a cyclic and chaotic way, and there can be more than one attractor for fixed parameters. We give examples of parameters for which four attractors coexist. For some parameters the dynamics is well described by iterates of a bimodal one dimensional map and we show that this map cannot have more than two attractors. The map is of general interest and can have two attractors only for a very small region of parameters. In all cases we discuss the birth of attractors through bifurcations and leave several interesting open questions.