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| Persistence and Extinction of a Stochastic Three-population Predation Model with Refuge and Ornstein-Uhlenbeck Process |
| SU Xiaoming, CHEN Bo
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| School of Science, Shenyang University of Technology, Shenyang 110870, China |
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Abstract Most current predation models describe the stochastic nature of the environment in terms of white noise, for the problem that the parameters in the model may satisfy the Ornstein-Uhlenbeck process in a real situation, a stochastic three-species predation model with refuge and Ornstein-Uhlenbeck process is proposed. The dynamic behavior of the model is analyzed by its formula, differential inequality and stochastic analysis theory. The existence and uniqueness of the global positive solution of the model are proved, sufficient conditions for the average persistence and extinction of each population were obtained separately, finally, python is used to carry out numerical simulation to verify the conclusions obtained in the theorem, and further study the impact of refuge on population size.
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Received: 19 May 2022
Published: 17 July 2024
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