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<p>This study analyzes bifurcation and stability dynamics in a discrete-time prey-predator system featuring a strong Allee effect in prey and ratio-dependent Holling type III functional response. Employing piecewise constant argument discretization, we derive a structurally consistent discrete model that preserves equilibria and bifurcation thresholds of its continuous-time counterpart. Bifurcation analysis and numerical simulations demonstrate that the strong Allee effect generates bistability regimes and extinction boundaries, while predator efficiency drives period-doubling cascades to chaos. Key findings reveal that increasing Allee thresholds enhances prey stability but amplifies sensitivity to initial conditions, creating critical conservation trade-offs. Hybrid chaos control stabilizes unstable manifolds, while state-feedback control suppresses chaotic oscillations through strategic eigenvalue relocation within the unit disk’s stability region. These mechanisms provide actionable insights for managing exploited populations near collapse thresholds, advancing predictive ecology through integration of discrete-time modeling with conservation imperatives for pulsed life-history systems.</p>

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Dynamics unveiled: investigating bifurcations and the strong Allee effect in a discrete-time prey-predator system

  • 期刊论文

  • 发表日期：

    2025年9月3日

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  • Hajar Mouhsine,
  • Halima Ben Ali,
  • Karima Mokni,
  • Mohamed Ch-Chaoui

摘要

This study analyzes bifurcation and stability dynamics in a discrete-time prey-predator system featuring a strong Allee effect in prey and ratio-dependent Holling type III functional response. Employing piecewise constant argument discretization, we derive a structurally consistent discrete model that preserves equilibria and bifurcation thresholds of its continuous-time counterpart. Bifurcation analysis and numerical simulations demonstrate that the strong Allee effect generates bistability regimes and extinction boundaries, while predator efficiency drives period-doubling cascades to chaos. Key findings reveal that increasing Allee thresholds enhances prey stability but amplifies sensitivity to initial conditions, creating critical conservation trade-offs. Hybrid chaos control stabilizes unstable manifolds, while state-feedback control suppresses chaotic oscillations through strategic eigenvalue relocation within the unit disk’s stability region. These mechanisms provide actionable insights for managing exploited populations near collapse thresholds, advancing predictive ecology through integration of discrete-time modeling with conservation imperatives for pulsed life-history systems.