Persistence and extinction of a modified Leslie-Gower Holling-type Ⅱ predator-prey stochastic model in polluted environments with impulsive toxicant input

Math Biosci Eng. 2021 Jun 3;18(4):4894-4918. doi: 10.3934/mbe.2021249.

Abstract

In this paper, a modified Leslie-Gower Holling-type Ⅱ two-predator one-prey stochastic model in polluted environments with impulsive toxicant input is proposed where we use an Ornstein-Uhlenbeck process to improve the stochasticity of the environment. The sharp sufficient conditions for persistence in the mean and extinction are established. The results reveal that the persistence and extinction of the species have close relationships with the toxicant and environmental stochasticity. In addition, the theoretical results are verified by numerical simulation.

Keywords: Itô's formula; extinction; intensity of white noise; persistence in the mean; stochastic models; toxicant effect.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Computer Simulation
  • Ecosystem
  • Food Chain
  • Hazardous Substances*
  • Models, Biological*
  • Population Dynamics
  • Predatory Behavior
  • Stochastic Processes

Substances

  • Hazardous Substances