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<p>This study proposes a Lotka–Volterra competition model incorporating a novel fear-based feedback control mechanism. Through theoretical analysis and numerical simulations, several important conclusions are obtained. The system admits at most two positive equilibria; while the feedback control parameter does not affect their existence, it plays a crucial role in determining their stability. A sufficiently large control intensity can enhance the stability of the positive equilibrium, thereby promoting species coexistence. The system exhibits rich bifurcation phenomena, including transcritical, pitchfork, saddle-node, Hopf, and Bogdanov–Takens bifurcations. Notably, a stable limit cycle may arise through a Hopf bifurcation. Under weak competition, the system admits at most one positive equilibrium, which is always stable regardless of the intensity of fear effects. In contrast, under strong competition, the system displays more complex dynamics, including the possible occurrence of multiple positive equilibria and intricate bifurcation structures. These results highlight the crucial role of fear-based feedback control in facilitating stable coexistence in competitive ecological systems.</p>

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Dynamical regulation of lotka-volterra competition systems: a novel fear-effect-based feedback control mechanism

  • 期刊论文

  • 发表日期：

    2025年7月10日

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  • Guangwen He,
  • Fengde Chen,
  • Zhong Li,
  • Lijuan Chen

摘要

This study proposes a Lotka–Volterra competition model incorporating a novel fear-based feedback control mechanism. Through theoretical analysis and numerical simulations, several important conclusions are obtained. The system admits at most two positive equilibria; while the feedback control parameter does not affect their existence, it plays a crucial role in determining their stability. A sufficiently large control intensity can enhance the stability of the positive equilibrium, thereby promoting species coexistence. The system exhibits rich bifurcation phenomena, including transcritical, pitchfork, saddle-node, Hopf, and Bogdanov–Takens bifurcations. Notably, a stable limit cycle may arise through a Hopf bifurcation. Under weak competition, the system admits at most one positive equilibrium, which is always stable regardless of the intensity of fear effects. In contrast, under strong competition, the system displays more complex dynamics, including the possible occurrence of multiple positive equilibria and intricate bifurcation structures. These results highlight the crucial role of fear-based feedback control in facilitating stable coexistence in competitive ecological systems.