Bifurcation and chaos of discretized Rosenzweig-MacArthur predator-prey model with Holling type II functional response

The growing interest in predator-prey dynamics has spurred the development of models that incorporate biological complexities arising from species interactions. This study systematically examines discrete-time predator-prey models with immigration, analyzing their equilibrium states, stability conditions, and bifurcation phenomena. Using analytical techniques from bifurcation theory and the center manifold theorem, we characterize Flip and Neimark-Sacker bifurcations, revealing how immigration influences system behavior near critical transitions. Numerical simulations complement theoretical results, demonstrating complex dynamical patterns through bifurcation diagrams. The findings provide a framework for understanding how immigration shapes predator-prey interactions, offering insights for ecological conservation and population management.