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<p>This paper proposes a stage-structured predator–prey model incorporating a fear response delay, where predators are divided into immature and mature stages. The model integrates the fear effect of mature predators on prey, hunting cooperation among mature predators and anti-predator behavior by prey against immature predators. We analyze the positivity and boundedness of solutions, the local stability of all equilibria and the permanence of the system. Furthermore, sufficient conditions for the global asymptotic stability of all non-trivial equilibria are established. Hopf bifurcation analysis around the coexistence equilibrium is performed, using the fear delay as the bifurcation parameter. Finally, numerical simulations are conducted to validate the analytical results.</p>

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Dynamics of a stage-structured predator–prey model with fear delay, hunting cooperation and anti-predator behavior

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Jixun Chu,
  • Ruiyi Wang,
  • Xiaofeng Zhang

摘要

This paper proposes a stage-structured predator–prey model incorporating a fear response delay, where predators are divided into immature and mature stages. The model integrates the fear effect of mature predators on prey, hunting cooperation among mature predators and anti-predator behavior by prey against immature predators. We analyze the positivity and boundedness of solutions, the local stability of all equilibria and the permanence of the system. Furthermore, sufficient conditions for the global asymptotic stability of all non-trivial equilibria are established. Hopf bifurcation analysis around the coexistence equilibrium is performed, using the fear delay as the bifurcation parameter. Finally, numerical simulations are conducted to validate the analytical results.