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<p>This paper proposes and analyzes the dynamics of a stochastic stage-structured predator-prey model that incorporates a fear delay and hunting cooperation. Predators are classified into immature and mature stages, and the model also accounts for intraspecific competition within both the prey and mature predator populations. We first establish the existence, uniqueness, and stochastic ultimate boundedness of a global positive solution. Sufficient conditions for extinction are derived for two scenarios: the survival of the prey species alongside the extinction of the predator, and the extinction of both species. Furthermore, criteria for the existence of a unique stationary distribution are established. Finally, numerical simulations are conducted to validate the analytical findings.</p>

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Dynamic of a Stochastic Stage-Structured Predator-Prey Model with Fear Delay and Hunting Cooperation

  • 期刊论文

  • 发表日期：

    2026年1月9日

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  • Jixun Chu,
  • Ruiyi Wang,
  • Xiaofeng Zhang

摘要

This paper proposes and analyzes the dynamics of a stochastic stage-structured predator-prey model that incorporates a fear delay and hunting cooperation. Predators are classified into immature and mature stages, and the model also accounts for intraspecific competition within both the prey and mature predator populations. We first establish the existence, uniqueness, and stochastic ultimate boundedness of a global positive solution. Sufficient conditions for extinction are derived for two scenarios: the survival of the prey species alongside the extinction of the predator, and the extinction of both species. Furthermore, criteria for the existence of a unique stationary distribution are established. Finally, numerical simulations are conducted to validate the analytical findings.