Complex dynamics of a discretized Rosenzweig–MacArthur prey-predator model with fear effect on prey and prey refuge

This work explores a discrete-time predator-prey system governed by a prey-dependent Rosenzweig–MacArthur response, incorporating the fear effect in prey dynamics. The study examines equilibrium properties and bifurcation mechanisms, particularly near the interior fixed point, highlighting their ecological significance. Various bifurcation types, including period-doubling and Neimark-Sacker, are identified, with precise conditions ensuring the latter's occurrence. To manage the system's intricate behavior, Ott-Grebogi-Yorke (OGY) and state feedback control are implemented. Numerical simulations reinforce theoretical findings through phase space reconstructions, Lyapunov exponent analysis, bifurcation diagrams, and local stability assessments, offering a comprehensive perspective on system transitions and control strategies.