Analysis And Study Of Biologic Protection Strategy Based On State Pulse Control

In the interference of human activities and the environment change,plant diseases and insect pests of species extinction and biological events happen very often.In order to maintain ecological diversity,the number of the predator-prey system in a certain range,this article through consulting a large number of literature,established reasonable prey-predator system model of impulsive differential equation,system periodic solution is obtained by theoretical proof of some meaningful conclusions.On the basis of a sort of HollingⅢ type predator-prey model by professor Qi-kuan Liu,a type of status impulsive differential equation is established.the existence and stability problems of the order 1 periodic solutions of state impulsive differential equation is studied.On the geometric theory of ordinary differential equations and subsequent function method,the control parameters and the pulse threshold in 5 kinds of different situations are discussed,the existence of sufficient conditions for the the system order 1 periodic solutions are got;Under the condition of existence of periodic solutions,the uniqueness of its existence and attract is studied.The rationality of the conclusion is verified by numerical simulation;The conclusions are the further research in a semi-continuous system by professor Qikuan Liu in "a class of prey-predator system with functional reaction model of qualitative analysis".This paper considered biological development and the practical significance of the control strategy,the control strategies from linear to nonlinear.The sufficient conditions of new model stability half of periodic solutions are obtained by structuring Poincare mapping;Using the similar Poincare mapping and other branches theory,two cases on the linear and nonlinear of the predator predator are discussed,the sufficient conditions of producing transcritical bifurcation are got.The rationality of the conclusion is verified by numerical simulation.The model and the conclusions are the further promotion of the single linear control strategy as the article Yulin Liu"a class of predator-prey system with HollingⅡ type functional response of pulse control”.