Study Of A Predator-Prey Model With State Dependent Impulsive Effect

It is well-known that the theory of impulsive differential equations is not only richer than the corresponding theory of differential equations but also represents a more natural framework for mathematical modeling of many real world phenomena. Significant progress has been made in the stability theory of impulsive differential equations in recent years. However, the corresponding qualitative theory for impulsive semi-dynamical systems is still stage of its development. In this paper, we will study one predator-prey model with state-dependent impulsive. In Chapter 1, some fundamental theories of semi-continuous dynamical . systems arc given. In Chapter 2, by the means of successor function, the order 1 periodic solution of the model with no explicit solution can be attained. At the end of the paper we find the sufficient condition for existence of the order 1 periodic solution and the order 2 periodic solution though a special predator-prey model. According to the Analogue of the Poincarc criterion, we show that order 1 periodic solution of the second model is orbitally asymptotically stable under some condition.