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” dynamicswith the preys’ intraspecific competition. The model has the form of the hybrid system consistingof the two two-dimensional systems switching between each other. The switching of the systemsallows us to reproduce the special Refuge-regime when the prey number is very small and thepredators have complications to find preys. The regularization of the system by using twoswitching lines to avoid chattering is provided. The limit sets for the regularized model areestablished. The model sensitivity to the switchings is investgated. The condition under which thehybridization does not change the global stability of an equilibrium is derived. In the other casethe limit sets are cycles.