Abstract. Autonomous systems of differential equations with variable structure and impulsive effects are the main objects of our study. The structure changes and the impulsive effects realize at the switching moments, which are specific to each different solution of the system. In these moments, the trajectory of the corresponding initial value problem meets successively the switching sets. For this class of equations, sufficient conditions for the existence of periodic solutions are found. The results are based on the Brouwer's fixed point theorem. We investigate the question of existence of periodic solutions of a generalized model of predator-prey community.

Received: May 2, 2015

AMS Subject Classification: 34A34

Key Words and Phrases: variable structure, impulses, switching functions, periodic solution

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