Dynamic Behavior of a Stochastic Predator Prey Model With the Gilpin-Ayala Growth

CHEN Qianjun; JIANG Yuan; LIU Zijian; TAN Yuanshun

doi:10.21656/1000-0887.420203

Volume 43 Issue 4

Apr. 2022

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CHEN Qianjun, JIANG Yuan, LIU Zijian, TAN Yuanshun. Dynamic Behavior of a Stochastic Predator Prey Model With the Gilpin-Ayala Growth[J]. Applied Mathematics and Mechanics, 2022, 43(4): 453-468. doi: 10.21656/1000-0887.420203

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Dynamic Behavior of a Stochastic Predator Prey Model With the Gilpin-Ayala Growth

doi: 10.21656/1000-0887.420203

College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P.R.China

Received Date: 2021-07-16
Rev Recd Date: 2022-03-05

Available Online: 2022-03-19

Publish Date: 2022-04-01

Abstract

Abstract

The dynamic behavior of a stochastic predator-prey model with the Gilpin-Ayala growth was studied. The existence and uniqueness of the global positive solution to the system were proved, and sufficient conditions for system extinction and persistence were obtained. On this basis, the thresholds for controlling the stochastic persistence and extinction of the predator-prey system were given, and some asymptotic behaviors of the solution were discussed. Finally, the effectiveness of the results was verified through numerical simulation.
- Gilpin-Ayala growth,
- predator-prey model,
- Markov switching,
- impulsive disturbance,
- persistence

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References(32)

References

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