Existence And Global Attractivity Of Periodic Solution For Several Class Of Differential And Difference Model

This paper studies a type of predator-prey system, one-order delayed differen-tial systems, and one-order difference equation. The results of one periodic solutionor several periodic solutions are established. The paper is divided into four chap-ters. Main contents are as follows:Chapter two is about a class of predator-prey model with functional responseand diffusion. By Mawhin's continuation theorem of coincidence theory and Lya-punov techniques , we get the suffcient conditions for the existence of one positiveperiodic solution and attractivity of periodic solution.In chapter three, we deal with a system of delayed differential equations. Bytheorem of fixed-point on cones, we get the existence of several periodic solutions.In chapter four, we discrete a differential model. Also, by Krasnselskii fixed-point theorem, we get the suffcient conditions of existence of one periodic solution.At the same time, the conditions of global attractivity for the solution are got.