The paper examines a problem of the optimal foraging theory, namely, the problem of choosing the most suitable patch by a population and finding the conditions for leaving it. The dynamics of the interactionbetween the predators and the preys is described by a modified Lotka –Volterra system taking into accountthe intraspecific competition among the prey and the feasibility of migration for the predator and the prey. Prey are assumed to have the possibility to migrate between patches. The paper furthers the approach of Charnov – Krivan taking into account the criticism concerning the impossibility for the population to have full information on the quality of all patches. This is done by posing the problem of finding optimal in the sense of the Nash equilibrium shares of the preystaying in the patch. Thus, the optimal behavior strategy is determined only for the patch currently occupied by the population. The hybrid system based on the Nash equilibrium is studied. The sufficient conditions for the invariance of a domain of the hybrid system’s phase space and stability of the equilibrium in this domain are determined.