Few Predator Persistence And Periodic Solution

This paper mainly devotes to studying the research on persistence and periodic of some classes of predator-prey systems. Sufficient conditions are derived that guarantee the persistence of the system and the existence of the positive periodic solution. The full text is composed of four parts, the concrete structure is as follows:In the first chapter, we introduce the history of mathematical ecology's development the existed related work and the origin of the problem we discussed. The main work of this paper is also simply introduced in the chapter. In the second chapter, a nonautomous prey-predator system with Holling-III and Beddington-type functional response is discussed in this paper. Sufficient conditions are derived that guarantee the persistence of the system, the existence and global asymptotic stability of the positive periodic solution. In the third chapter, a delayed multispecies ecological competition-predator system with Holling-III functional response is studied. By using the continuation theorem of coincidence degree theory, some sufficient conditions are derived for the existence, uniqueness positive periodic solutions to the system. Finally, in the fourth chapter, a predator-prey model with mutual interference is studied. Some sufficient conditions are obtained for the permanence for the model the differential in equality.