Kinetic Properties Of Several Types Of Ecological Systems

This dissertation mainly deals with dynamics of some population models by using Lyapunov function method and comparison theorem of ordinary differential equations, Floquet theorem and small amplitude perturbation skills of impulsive differential equations, continuation theorem of coincidence degree theory. These dynamics contain uniformly persistence, existence and stability of periodic solutions (or positive periodic solutions), ultimately boundedness and chaotic behavior of these systems. The paper is composed of four chapters.In Chapter 1, the historical background of problems to be studied and the significance of this dissertation are introduced. We summarize some excellent works in population dynamics. Then, we introduce some excellent works which emerge in recent years. In Chapter 2, the persistence of a ratio-dependent predator-prey model with stage structure is studied by using Lyapunov function method and comparison theorem. In Chapter 3, we consider the dynamic complexities of a predator-prey system with Holling type functional response and impulsive effects. We verify, when the impulsive period is no longer than some threshold, the pest-eradication solution is locally asymptotically stable. Otherwise, if the impulsive period is larger than the threshold, the system is permanent. Further influences of impulsive perturbations on the system are studied, and numerical simulation shows that the system has rich dynamical behaviors. In Chapter 4, a delayed ratio-dependent predator-prey model with Holling type functional response and impulse is investigated. By using the continuation theorem of coincidence degree theory, a set of easily sufficient conditions for the global existence of a positive periodic solution is established.