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<p>The predator–prey model discussed in this study incorporates a Holling type II functional response to both white and Lévy noises. It is shown that the system, with an initial positive value, possesses a unique positive solution. Subsequently, conditions are established to ensure the persistence and eventual extinction of prey and predator populations. An examination is carried out on the characteristics of the trajectory and the mean populations represented by the predator–prey system. The main findings derived are validated through an enhanced numerical method and several scenarios.</p>

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Dynamics of a stochastic model describing the interactions between prey and predator incorporating a Holling type II functional response with Lévy jumps

  • 期刊论文

  • 发表日期：

    2025年11月26日

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  • Nafia Aghoutane,
  • Mohamed Ben Said,
  • Lahcen Azrar

摘要

The predator–prey model discussed in this study incorporates a Holling type II functional response to both white and Lévy noises. It is shown that the system, with an initial positive value, possesses a unique positive solution. Subsequently, conditions are established to ensure the persistence and eventual extinction of prey and predator populations. An examination is carried out on the characteristics of the trajectory and the mean populations represented by the predator–prey system. The main findings derived are validated through an enhanced numerical method and several scenarios.