Stochastic resonance in underdamped periodic potential systems with alpha stable Lévy noise

Abstract In this paper, we investigate the effect of alpha stable Levy noise with alpha stability index α ( 0 α ≤ 2 ) on stochastic resonance (SR) in underdamped periodic potential systems by the non-perturbative expansion moment method and stochastic simulation. Using the spectral amplification factor as a quantifying index, we find that SR can occur in both sinusoidal potentials and ratchet potentials when α is close to 2, while the resonant effect becomes weaker as the stability index decreases. By means of massive numerical statistics, we ascribe this trend to the typical jumps of non-Gaussian Levy noise ( 0 α 2 ), which play a destructive role on the periodicity of the long time mean response. We also disclose that the skewness parameter of Levy noise has a more notable impact on the resonant effect of the asymmetric ratchet potential than that of the symmetric sinusoidal potential because of symmetry breaking.

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