Complex dynamics of a discrete-time Leslie–Gower predator–prey system with herd behavior and slow–fast effect on predator population

Abstract

This work examines a discrete Leslie–Gower predator–prey system with herd behavior, focusing on the influence of the slow–fast effect on predator dynamics. We analyze the presence and stability of fixed points, investigating period-doubling and Neimark–Sacker bifurcations at the positive fixed point. A hybrid control technique is implemented to successfully handle chaotic dynamics. Numerical simulations validate the theoretical findings, supporting our analysis. The parameter [Formula: see text] in the predator–prey system has a significant impact on system dynamics due to the slow–fast effect it represents. A stable positive fixed point signifies a lasting and balanced coexistence of predator and prey populations within a certain [Formula: see text] interval. Deviation from this range results in period-doubling and Neimark–Sacker bifurcations, increasing both unpredictability and instability in the system.