Suppression of oscillations by Levy noise

2009/10/11 by A. I. Olemskoĭ, A. I. Olemskoi, S. S. Borysov +5
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.0910.2018

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

openalex publication_date 2009/10/11 · arxiv created 2010/01/04 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find analytical solution of pair of stochastic equations with arbitrary forces and multiplicative Lévy noises in a steady-state nonequilibrium case. This solution shows that Lévy flights suppress always a quasi-periodical motion related to the limit cycle. We prove that difference between stochastic systems driven by Lévy and Gaussian noises is that the Lévy variation ΔL∼(Δt)^1/α with the exponent α<2 is much less than the Gaussian one ΔW∼(Δt)^1/2 in the Δt→ 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 (Δt)^2/α≪Δt.

Citations

• Pattern formation outside of equilibrium

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