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<p>In this paper, we study the dynamics of a discrete-time prey-predator model with a prey refuge. We establish the existence and stability of the equilibrium points of the model. It is proven that the system undergoes both flip (period-doubling) and Neimark-Sacker bifurcations, at the interior equilibrium point by using the center manifold theorem and bifurcation theory. Rich dynamical behavior is observed in the model, including invariant cycles, cascades of period-doubling bifurcation, and chaotic sets. Numerical simulations are performed to confirm the theoretical results, and indicate that the discrete model can display more complex dynamics compared to the corresponding continuous model.</p>

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Bifurcation analysis of a nonlinear discrete prey-predator system

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Hamza Rouah

摘要

In this paper, we study the dynamics of a discrete-time prey-predator model with a prey refuge. We establish the existence and stability of the equilibrium points of the model. It is proven that the system undergoes both flip (period-doubling) and Neimark-Sacker bifurcations, at the interior equilibrium point by using the center manifold theorem and bifurcation theory. Rich dynamical behavior is observed in the model, including invariant cycles, cascades of period-doubling bifurcation, and chaotic sets. Numerical simulations are performed to confirm the theoretical results, and indicate that the discrete model can display more complex dynamics compared to the corresponding continuous model.