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<p>This paper addresses a pursuit–evasion predator–prey model with alarm signal, which combines direct prey-taxis with the avoidance strategy that allows prey to move in the opposite direction of the alarm signal gradient generated by predators. The global existence and uniform boundedness of solutions to the model for general functional responses are proved by semigroup estimates. Then, the global stability of all constant steady states and their decay rates are obtained by establishing appropriate Lyapunov functionals.</p>

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Global dynamics of a pursuit–evasion predator–prey model with alarm signal

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Yafei Yang,
  • Meng Fan

摘要

This paper addresses a pursuit–evasion predator–prey model with alarm signal, which combines direct prey-taxis with the avoidance strategy that allows prey to move in the opposite direction of the alarm signal gradient generated by predators. The global existence and uniform boundedness of solutions to the model for general functional responses are proved by semigroup estimates. Then, the global stability of all constant steady states and their decay rates are obtained by establishing appropriate Lyapunov functionals.