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Precursor criteria for noise-induced critical transitions in multi-stable systems

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Abstract

Predicting noise-induced critical transitions between multi-stable states of a dynamical system is of uttermost importance in various fields. This paper investigates a tri-stable model with desirable, sub-desirable and undesirable states as a prototype class of real systems. Then, two critical transitions, from the desirable state to the sub-desirable one (CT1) and from the sub-desirable state to the undesirable one (CT2), induced by Gaussian white noise are uncovered. The new results show that the noise-induced CT1 and CT2 take place before the bifurcation point of the corresponding deterministic system and this phenomenon becomes earlier with increasing noise intensity. Therefore, some precursor criteria of the noise-induced CT1 and CT2 are further explored. Firstly, the largest Lyapunov exponent and the Shannon entropy are introduced into the prediction of the noise-induced CT1 and CT2 from a new perspective. It is found that both of them are more efficient compared to the classic variance and autocorrelation at-lag-1, and the Shannon entropy is more robust as compared to CT1 and CT2 under strong fluctuations. Moreover, a range of the bifurcation parameter, where noise-induced critical transitions may occur, is approximately quantified in the parameter-dependent basin of the unsafe regime. All of these results may provide some guidance for establishing more general precursor criteria of multiple noise-induced critical transitions in the future.

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Acknowledgments

This study was supported by the National Natural Science Foundation of China under Grant No. 11772255, the Fundamental Research Funds for the Central Universities, the Shaanxi Project for Distinguished Young Scholars, the Research Funds for Interdisciplinary Subject of Northwestern Polytechnical University and Shaanxi Provincial Key R&D Program 2020KW-013 and 2019TD-010. Y. Li thanks the China Postdoctoral Science Foundation funded project.

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, China

    Jinzhong Ma & Yong Xu

  2. MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an, 710072, China

    Yong Xu

  3. Center for Mathematical Sciences and School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Yongge Li

  4. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Ruilan Tian

  5. Department of Electrical Engineering, City University of Hong Kong, Hong Kong, 999077, China

    Guanrong Chen

  6. Potsdam Institute for Climate Impact Research, 14412, Potsdam, Germany

    Jürgen Kurths

  7. Department of Physics, Humboldt University at Berlin, 12489, Berlin, Germany

    Jürgen Kurths

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  1. Jinzhong Ma
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  2. Yong Xu
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Correspondence to Yong Xu.

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No conflict of interest exists in the submission of this manuscript, and manuscript is approved by all authors for publication. This work was original research, has not been published previously, and not under consideration for publication elsewhere in whole or in part.

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Ma, J., Xu, Y., Li, Y. et al. Precursor criteria for noise-induced critical transitions in multi-stable systems. Nonlinear Dyn 101, 21–35 (2020). https://doi.org/10.1007/s11071-020-05746-9

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