Turing Instability of Diffusive Predator-Prey System with Gompertz Growth

This paper mainly focus on the research of a predator-prey system with Gompertz growth of prey. When the system does not contain diffusion, the stability conditions of positive equilibrium and the occurring condition of the Hopf bifurcation are obtained. When the diffusion term of the system appears, the stable conditions of positive equilibrium and the Turing instability condition are also obtained. Turing instability is induced by the diffusion term through theoretical analysis. Thus, the region of parameters in which Turing instability occurs is presented. Then the amplitude equations are derived by the multiple scale method. The results will enrich the pattern dynamics in predator-prey systems.