Impulsive Controlfor Environmental Management

In the real world the model of differential equations play a very important role to describe various phenomena, which explains various system dynamics mode from mathematical point of view. Using differential equation theory, people can understand the internal laws of the real systems very well, and the systems can be controlled with the purpose of people.As in the real world, many of the systems have instantaneous changes, therefore, using impulsive differential equations to describe the system can reflect the system's internal rules more reasonably and more accurately.This article describes two types of impulsive differential systems, i. e., the impulsive differential system of the fixed time and the impulsive differential system depending on the state.This paper considers a pulse population model that be putted the natural enemies, insufflate chemical and catching in the fixed time. The existence and stability of periodic solution by impulsive differential equations theory and method are proved.As the solutions of pulse population model with the fixed time, after a period of time tend to zero, but the impule is still put into effect. In order to reduce costs we introduce impulsive differential equation model with the economic threshold and depending on state, and prove the existence of periodic solutions and stability of periodic of periodic solution.Finaly introduce a performance of system and analysis the asymptotic behavior of the target when the initial value is nearby the periodic solution.