Analysis of Effects of Delays and Diffusion on a Predator-Prey System

A reaction-diffusion predator-prey system with two delays is investigated. It is found that the spatially homogeneous periodic solution will occur when the sum of two delays crosses some critical values and Hopf bifurcation takes place. For the fixed domain and diffusion, some numerical simulations are also given to illustrate the theoretical analysis. In addition, special attention is paid to effects of diffusion on the bifurcating periodic solution. It is found that the diffusion would lead to the bifurcating period solution to destabilize by calculating the relevant expression of the Floquet exponent