Dynamics analysis of a discrete diffusion predator–prey model with prey refuge

Abstract

This paper investigates a discrete diffusion predator–prey model with periodic boundary conditions. Firstly, we analyze the existence conditions of the model’s equilibrium points, their local and global stability, and verify the uniform boundedness of its solutions. Subsequently, we establish the criteria for the occurrence of flip bifurcation and Neimark–Sacker bifurcation near the equilibrium points of the model. Additionally, we delve into chaos control theory and uncover the conditions for Turing instability in the discrete diffusion model under the effect of overall self-diffusion. Finally, through numerical simulations, we examine how temporal factors, diffusion coefficients, and the natural growth rate of prey influence the dynamic behavior of the system.