Abstract. In the paper we propose a Leslie model with impulsive state feedback control on the basis of the theory of economic threshold. Using the existence criteria of periodic solution of the general impulsive autonomous system, we obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for stability of periodic solution of order one are given by using stability criteria of periodic solution of the general impulsive autonomous system. Our results are confirmed by numerical simulations.

Received: May 16, 2011

AMS Subject Classification: 34C25, 92B05

Key Words and Phrases: Leslie model, state feedback control, globally asymptotical stability, periodic solution

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