Bifurcation and global stability of a discrete prey–predator model with saturated prey refuge

Abstract

This article aims to describe the qualitative behavior of a discrete‐time prey–predator model including prey refuge. It is assumed that the fraction of prey in refuge is a monotonically increasing but self‐limiting function of prey population. The fixed points of the system and their local stability are investigated. The criteria for Neimark–Sacker bifurcation and period‐doubling bifurcation are presented. The sufficient conditions for global asymptotic stability of the interior fixed point are derived. The chaotic behavior of the system is stabilized by applying a hybrid control strategy. We conclude with a numerical simulation that strengthens our theoretical discussion and provides a way to observe the complex behavior of the system.