Dynamics, Stability, and Bifurcation in Discrete-Time Predator-Prey Model

A discrete-time three-species food chain model is presented in this paper, focusing on bifurcation dynamics and chaos control. The transcritical and Neimark-Sacker bifurcations at distinct equilibrium points under specific parameter conditions are revealed by bifurcation and stability theory. Stabilizing chaotic dynamics is achieved using the Ott-Grebogi-Yorke (OGY) method. The dynamical behavior of the model is investigated by comparing phase portraits and time series across varying initial conditions. An assessment of stability is made, a topological classification is performed, and attractors are identified. Lyapunov exponent analysis also provides a deeper understanding of the system’s complex behavior. In food chain models based on population, numerical simulations verify theoretical results by revealing the complex interplay among bifurcations, chaos, and control mechanisms.