A model of hybrid population dynamics with refuge-regime: regularization and limit sets

The paper is devoted to the regularization of the population “predator—prey” dynamics with the preys' intraspecific competition. The model has the form of the hybrid system consisting of the two two-dimensional systems switching between each other. The switching of the systems allows us to reproduce the special Refuge-regime when the prey number is very small and the predators have complications to find preys. The regularization of the system by using two switching lines to avoid chattering is provided. The limit sets for the regularized model are established. The studying of the model sensitivity to the switchings. The condition under which the hybridization does not change the global stability of an equilibrium is derived. In the other case the limit sets are cycles.