|
|
|
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.
|
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: weixunpu@nwpu.edu.cn
|
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
|
[1] Burkett V R, Wilcox D A, Stottlemyer R, Barrow W, Fagre D, Baron J, Price J, Nielsen J L, Allen C D, Peterson D L, Ruggerone G and Doyle T 2005 Ecolog. Complex. 2 357
[2] Scheffer M, Carpenter S, Foley J A, Folke C and Walker B 2001 Nature 413 591
[3] Zhang H, Xu W, Han P and Qiao Y 2020 Phys. A 556 124809
[4] Zhang H, Xu W, Guo Q, Han P and Qiao Y 2020 Chaos Solitons Fract. 135 109767
[5] Zhang H, Xu W, Lei Y and Qiao Y 2019 Commun. Nonlinear Sci. Numer. Simulat. 77 258
[6] Schindler D W 1977 Science 195 260
[7] Carpenter S R 2005 Proc. Natl. Acad. Sci. USA 102 10002
[8] Carpenter S R, Ludwig D and Brock W A 1999 Ecolog. Appl. 9 751
[9] Carpenter S R, Caraco N F, Correll D L, Howarth R W, Sharpley A N and Smith V H 1998 Ecolog. Appl. 8 559
[10] Scheffer M, Brock W and Westley F 2000 Ecosystems 3 451
[11] Carpenter S and Brock W 2006 Ecology Lett. 9 311
[12] Dakos V, van Nes E H and Scheffer M 2013 Theoret. Ecology 6 309
[13] Wang R, Dearing J A, Langdon P G, Zhang E, Yang X, Dakos V and Scheffer M 2012 Nature 492 419
[14] Ma J, Xu Y, Kurths J, Wang H and Xu W 2018 Chaos 28 113601
[15] Ma J, Xu Y, Li Y, Tian R and Kurths J 2019 Chaos 29 081102
[16] Ma J, Xu Y, Xu W, Li Y and Kurths J 2019 Sci. China-Techn. Sci. 62 2144
[17] Li P, Nie L R, Huang Q R and Sun X X 2012 Chin. Phys. B 21 050503
[18] Ruyin C, Wanli P, Jianqiang Z and Linru N 2016 Chaos 26 093113
[19] Jianqiang Z, Linru N, Chongyang C and Xinyu Z 2016 AIP Advances 6 075212
[20] Chen R, Chen C and Nie L 2017 Int. J. Mod. Phys. B 31 1750259
[21] Chen R, Pan L, Nie L, Chen C, Zeng C and Liu S 2019 Indian J. Phys. 93 115
[22] I Freidlin M and D Wentzell A Random Perturbations of Dynamical Systems (Berlin, Heidelberg: Springer) p. 2012
[23] Chen H, Shen C, Zhang H and Kurths J 2017 Chaos 27 081102
[24] Chen X, Wu F, Duan J, Kurths J and Li X 2019 Appl. Math. Comput. 348 425
[25] Franovic I, Todorovic K, Perc M, Vasovic N and Buric N 2015 Phys. Rev. E 92 062911
[26] Tsiairis A, Wei P, Chao Y and Duan J 2021 Phys. A 569 125749
[27] Wells D K, Kath W L and Motter A E 2015 Phys. Rev. X 5 031036
[28] Folke C, Carpenter S, Walker B, Scheffer M, Elmqvist T, Gunderson L and Holling C S 2004 Annual Review of Ecology, Evolution, and Systematics 35 557
[29] Brock W and Carpenter S 2006 Ecology and Society 11 9
[30] Luchinsky D G and McClintock P V E 1997 Nature 389 463
[31] Maier R S and Stein D L 1996 J. Statist. Phys. 83 291
[32] Ludwig D 1975 Siam Review 17 605
[33] Beri S, Mannella R, Luchinsky D G, Silchenko A N and McClintock P V E 2005 Phys. Rev. E 72 036131
[34] Durr D and Bach A 1978 Commun. Math. Phys. 60 153
[35] Onsager L and Machlup S 1953 Phys. Rev. 91 1505
[36] Tisza L and Manning I 1957 Phys. Rev. 105 1695
[37] Chen Y, Gemmer J A, Silber M and Volkening A 2019 Chaos 29 043119 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
