Dynamic Analysis Of Two Classes Of Filippov Systems

In this thesis,with the help of differential inclusion theory,theory of differential equa-tions with discontinuous righthand sides and differential inequality technique,we investigate the dynamical behaviors of Filippov predator-prey model with prey refuge and Filippov SIR epidemic model with media coverage and vaccination,including the positive and bound-edness of solutions,the existence and stability of the equilibria in subsystems,the sliding mode dynamical behaviors on the switching line and the global dynamical behaviors of the system.The full thesis consists of the following four parts.In Chapter 1,the research background,significance and development status of predator-prey model with prey refuge and discontinuous epidemic model are introduced.The research contents,methods and some basic preliminaries of this thesis is briefly introduced as well.In Chapter 2,we discuss a Filippov predator-prey model with prey refuge.By employ-ing the Lyapunov function and inequality analysis techniques,the stability of the equilib-ria of the two subsystems are derived respectively.By using the differential inclusion and Filippov convex combination methods,the dynamic behaviors on the discontinuous bound-ary,including the existence of the sliding mode domain,the existence and the stability of the Pseudo-equilibrium are studied.The global dynamic behavior of the system is analyzed in different parameter regions.Finally,numerical simulations illustrate our results.In Chapter 3,considering the influence of media coverage and vaccination on the trans-mission mechanism of epidemic,on the basis of the traditional SIR epidemic model introduce two threshold strategies,we consider a Filippov SIR epidemic model with media coverage and vaccination.Firstly,by means of characteristic root analysis,Lyapunov function method and LaSalle invariance principle,we studied the stability of disease-free equilibrium and endemic equilibrium in the subsystem.Then,by using theory of differential equation with righthand sides,we investigate the sliding mode domain,the existence and stability of the pseudo-equilibria on the two switching lines.Finally,numerical simulation verifies the correctness of the theoretical results.Last but not least,our research work and the prospect of our future research are summarized.