Spatial Dynamics Of Two Class Of Periodic And Delayed Reaction-Diffusion Equation

To study the spatial dispersal of biological population and spread of the dis-ease,we usually establish appropriate mathematical models and do some quanti-tative analysis and simulation. These mathematical models can be boiled down to reaction-diffusion equations with time delays(nonlocal delays). In addition, we know that many populations is influenced greatly by the time varying envi-ronments composed by temperature, supply of food and water. Therefore, the study on non-autonomous reaction-diffusion systems is particularly realistic and important. This paper discusses two classes of periodic delayed reaction-diffusion equations with delay and studies their long time behavior using the method of dynamic system. In the first chapter, we introduce the background of the prob-lems discussed in this paper, and list some preliminaries on the periodic semi-flow theory. In the second chapter, we study a periodic reaction-diffusion model with nonlocal delay using persistence theory, and give the global existence of the the solutions and the uniformly persistent. In the third chapter, we consider the dynamics behavior of a non-autonomous systems which describe the spread of bacterial. By the analysis of the eigenvalue, we obtain the uniform persistence of the systems and global attractivity of the steady-state solution.