Existence And Stability Of Periodic Solutions For Some Predator-prey Models

In this dissertation, by using the generalized continuation theorem of coincidence degree theory, comparison principle of differential equations and Lyapunov function method, we obtain some sufficient criteria for the existence and multiplicity with stability of periodic solutions for three kinds of predator-prey biological models, which extending and developing some known results.The main organization of this paper is as follows:In chapter 1, we briefly introduce the research status of three kinds of biological models, the main work and some related basic knowleged in this paper.In chapter 2, by using the continuation theorem of coincidence degree theory,we obtain the existence condition of at least four periodic solutions for a delayed ratio-dependent predator-prey system. An example is represented to illustrate the feasibility of our main result.In chapter 3, we introduce the recent development and some results for the predator-prey model with stage structure.Secondly, sufficient conditions are derived for the uniform persistence of positive periodic solutions for this model. Thirdly sufficient conditions for the existence of positive periodic solutions for this model are obtained by using the continuation theorem of Gains and Mawhin.Finally, sufficient conditions for the global asymptotical stability of positive periodic solutions for this model are obtained by using Lyapunov function method, which extend some known results.In chapter 4, by using the continuation theorem of Gains and Mawhin, sufficient conditions for the existence of at leat four positive periodic solutions for an impulsive predator-prey model with Beddington-DeAngelis function and harvesting term are obtained.