Turing Stability Analysis in a Reaction-Diffusion Predator-Prey System with Fear Effect

In this paper, a Leslie-Gower predator-prey system with diffusion under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equation, the necessary and sufficient conditions for locally asymptotically stable and Turing instability of the positive equilibrium are given, respectively. Based on the stability theory of partial differential equations, this paper explores the influence of fear factor on the density of prey and predator population, and finds that the fear coefficient is inversely proportional to the population size. Numerical simulations are carried out to illustrate the main results.