The Phase Transition in a Bistable Duffing System Driven by Lévy Noise

Yong Xu; Yongge Li; Juanjuan Li; Jing Feng; Huiqing Zhang

doi:10.1007/s10955-014-1129-1

The Phase Transition in a Bistable Duffing System Driven by Lévy Noise

Yong Xu, Yongge Li, Juanjuan Li, Jing Feng, Huiqing Zhang

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

In this paper, the phase transition and mean first passage time (MFPT) induced by Lévy noise is investigated in a bistable Duffing system numerically. First, we obtain the stationary probability density functions as the criterion of phase transition through the qualitative changes of the shapes of stationary probability distribution. Then, the influences of Lévy noise parameters are discussed. The results indicate that the stability index, noise intensity and skewness parameter can lead to phase transition behaviors in bistable Duffing system. In addition, the MFPT is calculated for various Lévy parameters. Different effects among stability index, noise intensity and the skewness parameter on the phase transition and MFPT are observed. Furthermore, distinctions between Lévy noise and Gaussian noise are provided.

Original language	English
Pages (from-to)	120-131
Number of pages	12
Journal	Journal of Statistical Physics
Volume	158
Issue number	1
DOIs	https://doi.org/10.1007/s10955-014-1129-1
State	Published - Jan 2014

Keywords

Bistable Duffing system
Lévy noise
Mean first passage time (MFPT)
Phase transition
Stationary probability density

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10.1007/s10955-014-1129-1

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title = "The Phase Transition in a Bistable Duffing System Driven by L{\'e}vy Noise",

abstract = "In this paper, the phase transition and mean first passage time (MFPT) induced by L{\'e}vy noise is investigated in a bistable Duffing system numerically. First, we obtain the stationary probability density functions as the criterion of phase transition through the qualitative changes of the shapes of stationary probability distribution. Then, the influences of L{\'e}vy noise parameters are discussed. The results indicate that the stability index, noise intensity and skewness parameter can lead to phase transition behaviors in bistable Duffing system. In addition, the MFPT is calculated for various L{\'e}vy parameters. Different effects among stability index, noise intensity and the skewness parameter on the phase transition and MFPT are observed. Furthermore, distinctions between L{\'e}vy noise and Gaussian noise are provided.",

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author = "Yong Xu and Yongge Li and Juanjuan Li and Jing Feng and Huiqing Zhang",

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AB - In this paper, the phase transition and mean first passage time (MFPT) induced by Lévy noise is investigated in a bistable Duffing system numerically. First, we obtain the stationary probability density functions as the criterion of phase transition through the qualitative changes of the shapes of stationary probability distribution. Then, the influences of Lévy noise parameters are discussed. The results indicate that the stability index, noise intensity and skewness parameter can lead to phase transition behaviors in bistable Duffing system. In addition, the MFPT is calculated for various Lévy parameters. Different effects among stability index, noise intensity and the skewness parameter on the phase transition and MFPT are observed. Furthermore, distinctions between Lévy noise and Gaussian noise are provided.

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The Phase Transition in a Bistable Duffing System Driven by Lévy Noise

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Keywords

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