Dynamics Analysis of Prey–Predator Interactions with the Harvesting Effects on Both Predator and Prey Species

This study investigates the dynamic behaviors of a prey–predator model influenced by harvesting effects on both prey and predator species. The analysis identifies the fixed points of the system and characterizes their topological properties. Furthermore, the research demonstrates that the discrete-time prey–predator model can undergo Flip and Neimark–Sacker bifurcations under certain parametric conditions, applying bifurcation theory and the center manifold theorem. To control chaos, Ott–Grebogi–Yorke (OGY) feedback-control approach is implemented. Also, a comparative analysis is conducted between the dynamics of system (1), which excludes harvesting mechanisms as examined in examined in [Abbas & Khaliq, 2023], and those of system (2), where harvesting interventions are explicitly incorporated. Numerical simulations are provided to support the theoretical results and evaluate the effectiveness and practicality of the proposed chaos control strategy. The study includes bifurcation diagrams, phase portraits, maximum Lyapunov exponents, and a graph illustrating chaos control.