Suppression of oscillations by Levy noise

Details Suppression of oscillations by Levy noise Suppression of oscillations by Levy noise

2009-10-11

arxiv.org/abs/0910.2018v3

Physics

Condensed Matter

Statistical Mechanics

18 pages, 1 figure. Submitted to Fluctuation and Noise Letters

Scientific paper

We find analytical solution of pair of stochastic equations with arbitrary forces and multiplicative L\'evy noises in a steady-state nonequilibrium case. This solution shows that L\'evy flights suppress always a quasi-periodical motion related to the limit cycle. We prove that difference between stochastic systems driven by L\'evy and Gaussian noises is that the L\'evy variation $\Delta L\sim(\Delta t)^{1/\alpha}$ with the exponent $\alpha<2$ is much less than the Gaussian one $\Delta W\sim(\Delta t)^{1/2}$ in the $\Delta t\to 0$ limit. Moreover, this difference is shown to remove the problem of the calculus choice because related addition to the physical force is of order $(\Delta t)^{2/\alpha}\ll\Delta t$.

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