Complex dynamical regimes in the model of predator-prey communities coupled by migration with fast and slow cycles

The article considers the regimes that combine fast and slow cycles in the system of predator-prey communities coupled by migration, with the logistic growth of prey and nonlinear response of predators. We describe a periodic trajectory containing three different motions in phase space, which differ in periods of oscillation, as well as in the ratio of prey in different territories and synchronization between predators’ numbers. The emergence of such dynamics is probably connected with the « blue sky catastrophe ».