The phase transition in a bistable Duffing system driven by Lévy noise. (English) Zbl 1317.82036
Summary: 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.
MSC:
| 82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 34F05 | Ordinary differential equations and systems with randomness |
Keywords:
Lévy noise; bistable Duffing system; stationary probability density; phase transition; mean first passage time (MFPT)References:
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