Turing Instability of A Reaction-Diffusion Predator-Prey Model with Holling Type-II Function

The diffusion of population exists inevitably in predator-prey model due to the heterogeneity of space. The Turing instability of a predator-prey model with diffusion and Neumann boundary conditions is considered in this paper. Sufficient and necessary conditions are obtained for the diffusion-independent stability. We also perform a detailed analysis on the distribution of the characteristic roots for the system under diffusive effects. In addition, the conditions for the Turing instability are investigated. Numerical simulations are presented to illustrate the influence of spatial diffusion on the spatiotemporal dynamics.