Dynamical complexity of a spatial predator-prey system

Abstract

In this paper, we analyze the dynamical complexity of a spatial predator-prey system. We get the critical line of Hopf and Turing bifurcation in a spatial domain. Based on the mathematical analysis, we obtain the condition of the emergence of spatial patterns through diffusion instability, i.e., Turing pattern. The obtain results show that this system has rich dynamics, these patterns shows that it is useful the reaction-diffusion model to reveal the spatial dynamics in the real model.