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.