Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

doi:10.1007/s10483-021-2672-8

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (1): 65-84.doi: https://doi.org/10.1007/s10483-021-2672-8

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Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

Jinzhong MA¹, Yong XU^2,3, Yongge LI², Ruilan TIAN⁴, Shaojuan MA⁵, J. KURTHS^6,7

1. School of Mathematical Sciences, Shanxi University, Taiyuan 030000, China;
2. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
3. MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi'an 710072, China;
4. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
5. School of Mathematics & Information Science, North Minzu University, Yinchuan 750021, China;
6. Potsdam Institute for Climate Impact Research, Potsdam 14412, Germany;
7. Department of Physics, Humboldt University at Berlin, Berlin 12489, Germany

Received:2020-05-02 Revised:2020-07-15 Published:2020-12-19
Contact: Yong XU E-mail:hsux3@nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 12072264), the Fundamental Research Funds for the Central Universities, the Research Funds for Interdisciplinary Subject of Northwestern Polytechnical University, the Shaanxi Project for Distinguished Young Scholars, the National Key Research and Development Program of China (No. 2018AAA0102201), and the Shaanxi Provincial Key R&D Program (Nos. 2020KW-013 and 2019TD-010)

Abstract

Abstract: In real systems, the unpredictable jump changes of the random environment can induce the critical transitions (CTs) between two non-adjacent states, which are more catastrophic. Taking an asymmetric Lévy-noise-induced tri-stable model with desirable, sub-desirable, and undesirable states as a prototype class of real systems, a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out. We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability, which is named as the absorbed region. Then, a new concept of the parameter dependent basin of the unsafe regime (PDBUR) under the asymmetric Lévy noise is introduced. It is an efficient tool for approximately quantifying the ranges of the parameters, where the noise-induced CTs from the desirable state directly to the undesirable one may occur. More importantly, it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.

Key words: tri-stable model, asymmetric Lévy noise, critical transition (CT), escape probability, absorbed region, parameter dependent basin of unsafe regime (PDBUR)

2010 MSC Number:

Jinzhong MA, Yong XU, Yongge LI, Ruilan TIAN, Shaojuan MA, J. KURTHS. Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions. Applied Mathematics and Mechanics (English Edition), 2021, 42(1): 65-84.

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Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

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