Journal of Statistical Physics

, Volume 158, Issue 1, pp 120–131 | Cite as

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

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


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.


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



This work was supported by the NSF of China (11372247) and Shaanxi Province (2014JM1028), Program for NCET, the Fundamental Research Funds for the Central Universities (3102014JCQ01078) and NPU Foundation for Graduate Starting Seed.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Yong Xu
    • 1
  • Yongge Li
    • 1
  • Juanjuan Li
    • 1
  • Jing Feng
    • 1
  • Huiqing Zhang
    • 1
  1. 1.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anChina

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