### Mathematical Biosciences and Engineering

2021, Issue 4: 4894-4918. doi: 10.3934/mbe.2021249
Theory article

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

• Received: 25 March 2021 Accepted: 26 May 2021 Published: 03 June 2021
• 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.

Citation: Yongxin Gao, Shuyuan Yao. Persistence and extinction of a modified Leslie-Gower Holling-type Ⅱ predator-prey stochastic model in polluted environments with impulsive toxicant input[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 4894-4918. doi: 10.3934/mbe.2021249

### Related Papers:

• 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.

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