Existence of a polycycle in non-Lipschitz Gause-type predator–prey models

We study Gause-type predator–prey models when the interaction between predator and prey is not locally-Lipschitz continuous in the absence of one of them. We shall show that in this case there appears a polycycle, which affects the existence of limit cycles for the system. We apply the results to study the existence of limit cycles for a classical Gause system.