Dynamics Of Several Biomathematics Models With Impulses

In this thesis, by using theory of impulsive differential equations, we discuss the dy-namics of three predator-prey systems with impulses and study the permanence, existence and uniqueness of periodic solutions and global attractivity of those models, respectively. This article divided into four chapters.In Chapter1, we introduce some backgrounds of three impulsive predator-prey sys-tems, the main works of this thesis and some preliminary.In Chapter2, a ratio-dependent Leslie system with impulses is studied. By using the comparison theorem of impulsive differential equations, continuation theorem based on coincidence degree and constructing a suitable Lyapunov function, we establish sufficient and necessary conditions for the existence and global attractivity of periodic solution. An example shows that the obtained criteria is easily verifiable.In Chapter3, by using the comparison theorem, the method of coincidence degree and by constructing a suitable Lyapunov functional, we study the persistence, existence and attractivity of periodic solution for an N-species Gilpin-Ayala impulsive competition system. A set of sufficient conditions is obtained for the existence and global attractivity of periodic solution for the model. An Example shows the feasibility of our main results.In Chapter4, an impulsive periodic Holling-typeⅣ predator-prey system is con-sidered. By using Floquet theorem and small amplitude perturbation skills, a locally asymptotically stable prey-eradication periodic solution is obtained when the impulsive period is less than the critical value. Otherwise, if the impulsive period is larger than the critical value, the system is permanent. Finally, we conclude that our impulsive control strategy is more effective than the classical one if we take chemical control efficiently.