Exploring Ecological Dynamics and Bifurcation Structure of a Prey–Predator Model

The present work examines the dynamical features of a discrete-time Rosenzweig–MacArthur predator–prey system in which the predation rate is modulated by prey density. Through a combination of theoretical derivations and computational experiments, we establish the occurrence of period-doubling (PD) and Neimark–Sacker (NS) bifurcations, both of which culminate in chaotic regimes. The Lyapunov exponent spectrum corroborates this picture: Positive values mark the onset of chaos and reveal a pronounced dependence of the trajectories on parameter perturbations. Numerical simulations further reveal chaotic attractors and invariant closed trajectories. The Ott–Grebogi–Yorke (OGY) method is employed to stabilise unstable orbits to control chaos. When extending the analysis to a coupled network, we show that chaos appears beyond a certain critical coupling threshold. These insights advance understanding of predator–prey dynamics and chaos control in ecological systems.