Analysis of a stochastic fear effect predator-prey system with Crowley-Martin functional response and the Ornstein-Uhlenbeck process
This paper studied a stochastic fear effect predator-prey model with Crowley-Martin functional response and the Ornstein-Uhlenbeck process. First, the biological implication of introducing the Ornstein-Uhlenbeck process was illustrated. Subsequently, the existence and uniqueness of the global soluti...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241665 |
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| _version_ | 1832590765574848512 |
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| author | Jingwen Cui Hao Liu Xiaohui Ai |
| author_facet | Jingwen Cui Hao Liu Xiaohui Ai |
| author_sort | Jingwen Cui |
| collection | DOAJ |
| description | This paper studied a stochastic fear effect predator-prey model with Crowley-Martin functional response and the Ornstein-Uhlenbeck process. First, the biological implication of introducing the Ornstein-Uhlenbeck process was illustrated. Subsequently, the existence and uniqueness of the global solution were then established. Moreover, the ultimate boundedness of the model was analyzed. Then, by constructing the Lyapunov function and applying $ It\hat{o} $'s formula, the existence of the stationary distribution of the model was demonstrated. In addition, sufficient conditions for species extinction were provided. Finally, numerical simulations were performed to demonstrate the analytical results. |
| format | Article |
| id | doaj-art-a98438f8db794af1ac7600561ba9cfe9 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-a98438f8db794af1ac7600561ba9cfe92025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912349813500310.3934/math.20241665Analysis of a stochastic fear effect predator-prey system with Crowley-Martin functional response and the Ornstein-Uhlenbeck processJingwen Cui0Hao Liu1Xiaohui Ai2School of Science, Northeast Forestry University, Heilongjiang, ChinaSchool of Science, Northeast Forestry University, Heilongjiang, ChinaSchool of Science, Northeast Forestry University, Heilongjiang, ChinaThis paper studied a stochastic fear effect predator-prey model with Crowley-Martin functional response and the Ornstein-Uhlenbeck process. First, the biological implication of introducing the Ornstein-Uhlenbeck process was illustrated. Subsequently, the existence and uniqueness of the global solution were then established. Moreover, the ultimate boundedness of the model was analyzed. Then, by constructing the Lyapunov function and applying $ It\hat{o} $'s formula, the existence of the stationary distribution of the model was demonstrated. In addition, sufficient conditions for species extinction were provided. Finally, numerical simulations were performed to demonstrate the analytical results.https://www.aimspress.com/article/doi/10.3934/math.20241665ornstein-uhlenbeck processfear effectcrowley-martin functional responsestationary distributionextinction |
| spellingShingle | Jingwen Cui Hao Liu Xiaohui Ai Analysis of a stochastic fear effect predator-prey system with Crowley-Martin functional response and the Ornstein-Uhlenbeck process AIMS Mathematics ornstein-uhlenbeck process fear effect crowley-martin functional response stationary distribution extinction |
| title | Analysis of a stochastic fear effect predator-prey system with Crowley-Martin functional response and the Ornstein-Uhlenbeck process |
| title_full | Analysis of a stochastic fear effect predator-prey system with Crowley-Martin functional response and the Ornstein-Uhlenbeck process |
| title_fullStr | Analysis of a stochastic fear effect predator-prey system with Crowley-Martin functional response and the Ornstein-Uhlenbeck process |
| title_full_unstemmed | Analysis of a stochastic fear effect predator-prey system with Crowley-Martin functional response and the Ornstein-Uhlenbeck process |
| title_short | Analysis of a stochastic fear effect predator-prey system with Crowley-Martin functional response and the Ornstein-Uhlenbeck process |
| title_sort | analysis of a stochastic fear effect predator prey system with crowley martin functional response and the ornstein uhlenbeck process |
| topic | ornstein-uhlenbeck process fear effect crowley-martin functional response stationary distribution extinction |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241665 |
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