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<p>This study examines the discrete-time dynamics of a predator-prey model incorporating an Ivlev functional response with an Allee effect. Through rigorous algebraic analysis, we establish the occurrence of period-doubling (PD) and Neimark–Sacker (NS) bifurcations in the positive phase space. Using the center-manifold theorem and bifurcation theory, we provide a theoretical framework to understand these bifurcations. Numerical simulations confirm our findings, illustrating chaotic behavior through phase portraits, period-12 orbits, invariant closed curves, and chaotic attractors. Lyapunov exponents further validate the chaotic nature of the system, emphasizing the influence of parameter variations on dynamic transitions. To mitigate chaos, we implement an OGY control strategy, effectively stabilizing trajectories around an unstable equilibrium. Furthermore, we extend the analysis to a coupled predator-prey network, revealing that chaotic behavior emerges when the coupling strength exceeds a critical threshold. Stochastic simulations, employing the Euler-Maruyama method, account for environmental uncertainties and explore system behavior under varying ecological conditions. This research advances the understanding of non-linear predator-prey interactions, bifurcations, and chaotic transitions in isolated and networked systems while demonstrating effective strategies for controlling instability in ecological dynamics.</p>

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Bifurcation Analysis, Chaos Control and Complex Dynamics of a Discrete Prey-Predator System Incorporating an Ivlev Functional Response with an Allee Effect

  • 期刊论文

  • 发表日期：

    2025年7月2日

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  • Md. Mutakabbir Khan,
  • Md. Jasim Uddin,
  • Parvaiz Ahmad Naik,
  • Zohreh Eskandari,
  • Zhengxin Huang

摘要

This study examines the discrete-time dynamics of a predator-prey model incorporating an Ivlev functional response with an Allee effect. Through rigorous algebraic analysis, we establish the occurrence of period-doubling (PD) and Neimark–Sacker (NS) bifurcations in the positive phase space. Using the center-manifold theorem and bifurcation theory, we provide a theoretical framework to understand these bifurcations. Numerical simulations confirm our findings, illustrating chaotic behavior through phase portraits, period-12 orbits, invariant closed curves, and chaotic attractors. Lyapunov exponents further validate the chaotic nature of the system, emphasizing the influence of parameter variations on dynamic transitions. To mitigate chaos, we implement an OGY control strategy, effectively stabilizing trajectories around an unstable equilibrium. Furthermore, we extend the analysis to a coupled predator-prey network, revealing that chaotic behavior emerges when the coupling strength exceeds a critical threshold. Stochastic simulations, employing the Euler-Maruyama method, account for environmental uncertainties and explore system behavior under varying ecological conditions. This research advances the understanding of non-linear predator-prey interactions, bifurcations, and chaotic transitions in isolated and networked systems while demonstrating effective strategies for controlling instability in ecological dynamics.