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.