Study On The Stability Of Impulsive Predator-Prey System With Mutual Interference And Numerical Analysis

With the development of society and the destruction of ecological environment,the stability of ecosystem has been paid more and more attention.Because of the complexity of the ecological environment,it is often necessary to consider the influence of interaction between population and the impulsive control strategies from human being.In this paper,we study the stability of three kinds of impulsive predator-prey systems with mutual interference,which are mainly composed of the following five chapters.The first chapter introduces the research background,research significance and research status at home and abroad.In the second chapter,we introduce the basic knowledge of systems,some definitions,theorems and lemmas are given to prove the boundedness of systems,the existence and globally asymptotic stability of prey extinction periodic solution and permanence.In the third chapter,we mainly study the stability of a class of impulsive predator-prey system with mutual interference.By using stability theory of impulsive differential equations,theory of biological systems and comparison method,the existence and globally asymptotic stability of prey extinction periodic solution and sufficient conditions for permanence of the system are obtained.Then numerical simulation is used to analyze the stability of this system,and complex dynamic behavior of this system is further discussed.Finally,from the point of view of biological theory,biological significance of these results is analyzed,and some feasible control strategies and suggestions are given.In the fourth chapter,we consider a class of impulsive three species predator-prey model with square root functional response and mutual interference.By using techniques of impulsive perturbations,Floquet theory,inequality theory and comparison theorem,the existence and global asymptotic stability of prey-eradication periodic solution are investigated.The sufficient conditions for the permanence of this system are discussed by means of appropriate Lyapunov functions and comparison theorem.Finally,the influence of interference coefficient and impulsive period on the stability is discussed by numerical simulation.The fifth chapter is based on the actual situation,taking into account chemical control and biological control at different times,mutual interference between predators and other factors on the actual impact of population,a class of impulsive three species predator-prey model is established.Sufficient conditions for the extinction of prey and persistence of this system are obtained by using some related theories.Then,numerical simulations are carried out to study the dynamic properties of this system.Finally,the biological significance of these results is given,and some suggestions based on the relevant control strategies are given.In a word,through theoretical analysis on the above system,the existence of periodic solutions,stability and persistence of these systems are investigated.Our obtained results extend or improve some existing theoretical results,and enrich the theory of impulsive differential system and biological dynamical system.By numerical simulation,the influence of interference factor,impulsive factor and functional responses on the dynamic properties of these systems is further studied,which reveals the complex dynamical properties of these systems.We gives some control strategies and suggestions for system control and ecological balance protection.The obtained results have good theoretical significance and practical significance.