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<p>A stochastic differential equation model, which describes the evolution of a polluted population incorporating environmental perturbations and Allee effect, is proposed and analyzed. First, it is proved that there is a unique global positive solution to the model. Then persistence and extinction of the population are obtained, and the persistence-and-extinction threshold is provided. Furthermore, the growth rate of the species is explored. The theoretical results indicate that environmental perturbations, Allee effect and pollution play significant roles on the dynamical behaviours of the model. In the end, biological explanations of the theoretical results are presented by the aid of numerical simulations.</p>

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Mathematical Modelling and Properties of Stochastic Polluted Population Dynamics with Allee Effect

  • 期刊论文

  • 发表日期：

    2025年1月23日

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  • Jing Ge,
  • Meng Liu

摘要

A stochastic differential equation model, which describes the evolution of a polluted population incorporating environmental perturbations and Allee effect, is proposed and analyzed. First, it is proved that there is a unique global positive solution to the model. Then persistence and extinction of the population are obtained, and the persistence-and-extinction threshold is provided. Furthermore, the growth rate of the species is explored. The theoretical results indicate that environmental perturbations, Allee effect and pollution play significant roles on the dynamical behaviours of the model. In the end, biological explanations of the theoretical results are presented by the aid of numerical simulations.