Review of the behaviour of a many predators-one prey system.

We consider a known predator-prey system, where more than one predator compete for the same prey. Mainly the case with two predators is considered. A review of general results is given, among them conditions for the extinction of one predator and an investigation of the different types of coexistence of predators. In non-degenerate cases the predators in this model cannot coexist at an equilibrium, but there can be a cyclic or more complicated coexistence. Many numerical results are presented. A model map for a Poincar´e map is given under some conditions. But the most interesting case where there can arise ”spiral-like” attractors is not well known here, and we pose open questions. We discuss some bifurcations and the existence of systems with several attractors.