Complex Dynamics of a Discrete Prey–Predator Model Exposing to Harvesting and Allee Effect on the Prey Species with Chaos Control

Abstract

This study discusses the dynamic behaviors of the prey–predator model subject to the Allee effect and the harvesting of prey species. The existence of fixed points and the topological categorization of the co-existing fixed point of the model are determined. It is shown that the discrete-time prey–predator model can undergo Flip and Neimark–Sacker bifurcations under some parametric assumptions using bifurcation theory and the center manifold theorem. A chaos control technique called the feedback-control method is utilized to eliminate chaos. Numerical examples are given to support the theoretical findings and investigate chaos strategies’ effectiveness and feasibility. Additionally, bifurcation diagrams, phase portraits, maximum Lyapunov exponents, and a graph showing chaos control are demonstrated.