Most probable transition paths in eutrophicated lake ecosystem under Gaussian white noise and periodic force

doi:10.1088/1674-1056/ac5616

中国物理B ›› 2022, Vol. 31 ›› Issue (6): 60203-060203.doi: 10.1088/1674-1056/ac5616

Most probable transition paths in eutrophicated lake ecosystem under Gaussian white noise and periodic force

Jinlian Jiang(姜金连), Wei Xu(徐伟)^†, Ping Han(韩平), and Lizhi Niu(牛立志)

School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2021-11-05 修回日期:2022-01-12 接受日期:2022-02-17 出版日期:2022-05-17 发布日期:2022-05-19
通讯作者: Wei Xu E-mail:weixunpu@nwpu.edu.cn
基金资助:
Projected supported by the National Natural Science Foundation of China (Grant Nos. 12072261 and 11872305).

Most probable transition paths in eutrophicated lake ecosystem under Gaussian white noise and periodic force

Jinlian Jiang(姜金连), Wei Xu(徐伟)^†, Ping Han(韩平), and Lizhi Niu(牛立志)

School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2021-11-05 Revised:2022-01-12 Accepted:2022-02-17 Online:2022-05-17 Published:2022-05-19
Contact: Wei Xu E-mail:weixunpu@nwpu.edu.cn
Supported by:
Projected supported by the National Natural Science Foundation of China (Grant Nos. 12072261 and 11872305).

摘要/Abstract

摘要： The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored. Unlike the existing work in detecting early warning signals, this paper presents the most probable transition paths to characterize the regime shifts. The most probable transition paths are obtained by minimizing the Freidlin-Wentzell (FW) action functional and Onsager-Machlup (OM) action functional, respectively. The most probable path shows the movement trend of the lake eutrophication system under noise excitation, and describes the global transition behavior of the system. Under the excitation of Gaussian noise, the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths. Under the excitation of Gaussian white noise and periodic force, we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution.

关键词: eutrophicated lake ecosystem, Freidlin-Wentzell action functional, Onsager-Machlup action functional, most probable transition path

Abstract: The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored. Unlike the existing work in detecting early warning signals, this paper presents the most probable transition paths to characterize the regime shifts. The most probable transition paths are obtained by minimizing the Freidlin-Wentzell (FW) action functional and Onsager-Machlup (OM) action functional, respectively. The most probable path shows the movement trend of the lake eutrophication system under noise excitation, and describes the global transition behavior of the system. Under the excitation of Gaussian noise, the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths. Under the excitation of Gaussian white noise and periodic force, we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution.

Key words: eutrophicated lake ecosystem, Freidlin-Wentzell action functional, Onsager-Machlup action functional, most probable transition path

中图分类号: (Probability theory, stochastic processes, and statistics)

02.50.-r

02.50.Fz (Stochastic analysis) 02.60.Cb (Numerical simulation; solution of equations)

Jinlian Jiang(姜金连), Wei Xu(徐伟), Ping Han(韩平), and Lizhi Niu(牛立志). Most probable transition paths in eutrophicated lake ecosystem under Gaussian white noise and periodic force[J]. 中国物理B, 2022, 31(6): 60203-060203.

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Most probable transition paths in eutrophicated lake ecosystem under Gaussian white noise and periodic force

Most probable transition paths in eutrophicated lake ecosystem under Gaussian white noise and periodic force

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