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<p>This paper investigates a hybrid predator–prey model with Beddington-DeAngelis functional response including one prey and two predator, extending the classical deterministic framework to account for environmental noise and regime switching. We first establish the existence-uniqueness for a global positive solution, along with its ultimate boundedness. Given the ecological significance of long-term species survival, we derive sufficient conditions for the persistence and extinction of all three interacting populations. Furthermore, by constructing a suitable Lyapunov function, we prove the existence of a unique stationary distribution, characterizing the system’s long-term behavior. The results of the numerical simulations are provided to validate the theoretical findings, demonstrating the interplay between stochastic perturbations and population dynamics.</p>

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A hybrid predator–prey model with Beddington-DeAngelis functional response involving teams of one prey and two predators

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Jingyi Zhao,
  • Yongchang Wei

摘要

This paper investigates a hybrid predator–prey model with Beddington-DeAngelis functional response including one prey and two predator, extending the classical deterministic framework to account for environmental noise and regime switching. We first establish the existence-uniqueness for a global positive solution, along with its ultimate boundedness. Given the ecological significance of long-term species survival, we derive sufficient conditions for the persistence and extinction of all three interacting populations. Furthermore, by constructing a suitable Lyapunov function, we prove the existence of a unique stationary distribution, characterizing the system’s long-term behavior. The results of the numerical simulations are provided to validate the theoretical findings, demonstrating the interplay between stochastic perturbations and population dynamics.