Predator-Prey Model With Reaction-Diffusion

The study of biological problems has become one of the important directions of the present life science with the rich mathematical theory and methods by establishing the bio-mathematical model. Concerning the influence of proliferation factors on population dynam-ics in the ecological environment of different patches, this paper would study the mathematical model of the reaction-diffusion equation with time delay.In chapterâ… , we introduce some knowledge of biology mathematics and the main work.In chapterâ…¡, we demonstrate local asymptotic stability and global asymptotic stability of equilibrium solutions of a predator-prey model with time delay.In chapterâ…¢, we take reaction-diffusion equations into consideration based on the model of the second chapter. First, it gives the local asymptotic stability of equilibrium solution reflecting reaction-diffusion equation. Then, it proves the existence of traveling solutions.