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

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.