Exploring complex dynamics in a Ricker type predator–prey model with prey refuge

This study examines the complexities of a discrete-time predator–prey model by integrating the impact of prey refuge, with the goal of providing a more realistic understanding of predator–prey interactions. We explore the existence and stability of fixed points within the model, offering a thorough examination of these critical aspects. Furthermore, we use center manifold and bifurcation theory to thoroughly analyze the presence and direction of period-doubling and Neimark–Sacker bifurcations. We also provide numerical simulations to validate our theoretical findings and demonstrate the intricacy of the model. The findings suggest that the inclusion of prey refuge has a notable stabilizing impact on the predator–prey model, hence enhancing the overall stability and resilience of the ecosystem.