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Chin. Phys. B, 2022, Vol. 31(6): 060203    DOI: 10.1088/1674-1056/ac5616
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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
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.
Keywords:  eutrophicated lake ecosystem      Freidlin-Wentzell action functional      Onsager-Machlup action functional      most probable transition path  
Received:  05 November 2021      Revised:  12 January 2022      Accepted manuscript online:  17 February 2022
PACS:  02.50.-r (Probability theory, stochastic processes, and statistics)  
  02.50.Fz (Stochastic analysis)  
  02.60.Cb (Numerical simulation; solution of equations)  
Fund: Projected supported by the National Natural Science Foundation of China (Grant Nos. 12072261 and 11872305).
Corresponding Authors:  Wei Xu     E-mail:

Cite this article: 

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 2022 Chin. Phys. B 31 060203

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