Stability, bifurcation analysis and pattern formation for a nonlinear discrete predator–prey system

Abstract

This work investigates a discrete predator–prey system with periodic boundary conditions. First, the existence, local stability, and global stability of the equilibrium points of the system are investigated. Second, we get the criteria for flip bifurcation and Neimark–Sacker bifurcation at the system’s equilibrium points, and we obtain the conditions for the Turing instability of the discrete diffusion system when the population self-diffusion occurs. Finally, we use numerical simulation to investigate the effect of the diffusion coefficient and the natural growth rate of prey on system dynamics.