Qualitative And Stability Analysis For Two Classes Of Ecological Dynamical Systems With Discontinuous Harvesting Policies

In this paper, we introduce two classes of predator-prey systems, with discon-tinuous harvesting policies. Based on the differential inclusions theory, topological theory in set-valued analysis and generalized Lyapunov approach, we analyze the persistence, existence of positive periodic solutions, existence and global asymp-totic stability of the positive solutions. This paper is composed of four chapters.In the first chapter, we introduced the historical background and the devel-opment of the functional response functions and discontinuous harvesting policies of mathematical system. Then, we summarized the main work of the paper.In the second chapter, we introduced the preliminaries of the paper.In the third chapter, a class of predator-prey system with Beddington-DeAnglis functional response and discontinuous harvesting policy is discussed. Firstly, By using the theory of the differential theory, we defined the solution for the system with a discontinuous right-hand side. Then, based on topological degree theory in set-valued analysis and Lyapunov approach, some sufficient conditions are ob-tained to guarantee the persistence, the existence of positive periodic solutions, the existence and global asymptotic stability of positive the positive solution for the system.In the forth chapter, we studied the persistence, and the global asymptotic stability of a class of predator-prey system with Michaelis-Menten functional re-sponse and discontinuous harvesting policy in brief.