Anomalous Dynamics of Inertial Systems Driven by Colored Lévy Noise

  • Yan LüEmail author
  • Hong Lu


Dynamics of underdamped particles subjected to colored Lévy noise is investigated analytically. The probability density distribution of the Lévy particle in the harmonic potential is exactly obtained by solving the fractional Fokker–Planck equation, which is also a Lévy type one with width depends on both correlation time \(\tau _c\) and damping coefficient \(\gamma \) and converges to the distribution for the white-noise, overdamped case in the limit \(\tau _c\rightarrow 0\), \(\gamma \rightarrow \infty \). Moreover, we obtain an analytical expression of escape rate for the underdamped particle escaping from a metastable potential by using the reactive flux method. It is shown that the stationary escape rate exhibits nonmonotonic dependence on the Lévy index, while an increase of the noise correlation time leads to the monotonic decrease of escape rete.


Lévy flight Colored Lévy noise Escape rate Metastable potential 



This work was supported by the Special Foundation for Theoretical Physics under Grant No. 11447186 and and the Doctoral Scientific Research Starting Foundation of Taiyuan University of Science and Technology (Grant No. 20122042).


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Authors and Affiliations

  1. 1.School of Applied ScienceTaiyuan University of Science and TechnologyTaiyuanChina
  2. 2.School of ScienceGuizhou University of engineering scienceBijieChina

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