The Application Of Impulse In Dynamic System

Impulsive differential equation presents the quick change or jump of some states of motion at the fixed or varied time. It reflects the developing process of nature more actually. Impulsive control of biological population becomes an interesting and challenging research task in the fields of biological control, so, impulsive differential equation has shown all-right applicative prospect in the study of population dynamics.First, the wide applications of impulsive differential systems are introduced, which shows the theoretical significance and practical value of the research, introduces some related results to the stability of solutions of impulsive differential systems.Second, by means of Lyapunov methods, we apply Schaefer fixed point theorem to prove the local existence of the solution, and obtain the sufficient conditions of exponentially stability.Finally, a class population dynamical with the impulsive control was investigated. we investigate a delayed stage-structured Monod-Haldane predator-prey model with impulsive stocking on prey and continuous harvesting on predator. Sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system are obtained.