Dynamics Analysis Of Some Biomathematics Models

This thesis mainly deals with dynamics of some kinds of biological models by using the generalized continuation theorem of coincidence degree theory, differential inequality theory, Lyapunov function method, these dynamics properties including:uniqueness of periodic solutions, existence of multiply solutions, existence and stability of a positive asymptotically periodic solution. The organization of this thesis is as follows. This paper is composed of four chapters:In Chapter1, we introduce the development of biomathematics, the historical back-grounds and the main works of three kinds of biological models, the works that many authors have done on them and some basic knowledge.In Chapter2, a delayed Holling II type predator-prey models with feedback controls is investigated. By using the generalized continuation theorem of coincidence degree theory, we get the sufficient conditions which guarantee the existence of periodic solution, what’s more, it extend and develop some known results.In Chapter3, a ratio-dependent predator-prey model with time delays is investigated. By using the generalized continuation theorem of coincidence degree theory, a new result of the existence of at least two positive periodic solutions is obtained. Finally, an example is given to illustrate our main results, which extend some known results.In Chapter4, a N-species cooperation system with time-varying delays is investi-gated. By using differential inequality theory, we obtain the permanence of this sys-tem.constructing a suitable Lyapunov function, we get the sufficient conditions which guarantee the existence and stability of a positive asymptotically periodic solution.