Dynamic Analysis Of Predator-prey Systems With Functional Response Under Discontinuous Harvesting Policy

This paper extends the theory of differential equation with discontinuous right-hand sides by combing the theory of differential inclusion,set-valued mapping and differential inequality technique.After,we observe the interaction between predator and prey,establish a class predator-prey model which can be described by discontinuous differential equation.By using the theory of differential equation with discontinuous right-hand sides,we analyze the dynamical behaviors of this model.The results play an important role in achieving sustainable development of resources.This paper is divided into four chapters.In the first chapter,we first have a view on the history and development of the theory of discontinuous differential equation,then we introduce the application and development of the research history of discontinuous biological dynamical systems,after we explain the motivation and significance of this study,finally we just briefly introduce the research content of this article.In the second chapter,we mainly define the solution of the differential equation with discontinuous right sides in Filippov sense,elaborate set-valued mappings,non-smooth analysis and some related theoretical knowledge.The knowledge provide a theoretical basis for studying the properties of the equations,we also have a knowledge of the methods to prove the convergence of differential equation with discontinuous right-hand sides.In the third chapter,we investigate the dynamics of two class of predator-prey system with Holling type functional response under discontinuous harvesting policy.Based on the inequality technique,the topological degree theory and fixed point theorem of set-valued mappings and the generalized Lyapunov theory,we study the consistent persistence of the autonomous system,analyze the existence for the positive equilibrium of the autonomous system and the periodic solutions of the nonautonomous system,we also discuss the global asymptotic stability for the positive equilibrium of the autonomous system and the global convergence for the periodic solutions of the non-autonomous system.In the fourth chapter,with the help of the theory of differential inclusions,a class discontinuous predator-prey system with ratio dependence,Gause type functional response and time-delay is described.By using the Mawhin fixed point theorem of set-valued mappings,we discuss the existence for positive periodic solution of the system,then we analyze global asymptotic stability for the positive periodic solution and the global convergence in measure for the harvesting solution by constructing suitable generalized Lyapunov function for the system.