Open AccessSuppression of Oscillations by Lévy Noise
Author(s) -
A. I. Olemskoĭ,
Stanislav S. Borysov,
I. A. Shuda
Publication year - 2022
Publication title -
ukrainian journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.213
H-Index - 17
eISSN - 2071-0194
pISSN - 2071-0186
DOI - 10.15407/ujpe56.3.287
Subject(s) - quasiperiodic function , limit (mathematics) , exponent , multiplicative function , limit cycle , physics , gaussian , noise (video) , multiplicative noise , non equilibrium thermodynamics , mathematical physics , statistical physics , mathematical analysis , mathematics , quantum mechanics , condensed matter physics , linguistics , philosophy , engineering , signal transfer function , digital signal processing , artificial intelligence , computer science , analog signal , electrical engineering , image (mathematics)
We find the analytic solution of a pair of stochastic equations with arbitrary forces and multiplicative Lévy noises in a steady-state nonequilibrium case. This solution shows that Lévy flights always suppress a quasiperiodic motion related to the limit cycle. We prove that such suppression is caused by that the Lévy variation ∆L ~ (∆t)1/α with the exponent α < 2 is always negligible in comparison with the Gaussian variation ∆W ~ (∆t)1/2 in the ∆t → 0 limit.