Chaotic dynamics and control in a discrete predation model with Holling II and prey refuge effects

Understanding predator-prey interactions is crucial for modeling ecological systems. This study investigates a discrete-time predator-prey system with a Holling type II functional response and prey refuge. Linear stability analysis establishes existence conditions and stability criteria for equilibrium points, while bifurcation analysis reveals critical transitions through period-doubling and Neimark-Sacker bifurcations. The center manifold theorem facilitates dimensionality reduction, enabling precise characterization of local dynamics near bifurcation points. Comprehensive numerical simulations—including bifurcation diagrams, phase portraits, maximum Lyapunov exponents, and time series—validate theoretical predictions and uncover complex behavioral regimes. A state feedback control strategy, derived from triangular stability regions, effectively suppresses chaotic fluctuations and stabilizes the system. These results advance fundamental understanding of ecological dynamics while offering practical stabilization techniques, bridging mathematical theory with applied ecological management. The interdisciplinary framework provides actionable insights for maintaining balance in complex ecological systems.