Open AccessStochastic resonance of a memorial-damped linear system with natural frequency fluctuation
Author(s) -
Xie Wen-Xian,
Dongping Li,
Pan Xu,
Cai Li,
Jin Yan-Fei
Publication year - 2014
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.63.100502
Subject(s) - stochastic resonance , noise (video) , laplace transform , kernel (algebra) , resonance (particle physics) , spectral density , exponential function , amplitude , physics , langevin equation , statistical physics , mathematical analysis , mathematics , computer science , quantum mechanics , statistics , artificial intelligence , image (mathematics) , combinatorics
The stochastic resonance is investigated in the generalized Langevin equation with exponential memory kernel subjected to the joint action of internal noise, external noise and external sinusoidal forcing. The system is converted into three-dimensional Markovian Langevin equations. Furthermore, using the Shapiro-Loginov formula and the Laplace transformation technique, the exact expressions of the first moment and the steady response amplitude are obtained. The research results show that with the variations of external sinusoidal force frequency and the parameters of memory kernel and external noise, the system presents bona-fide stochastic resonance, conventional stochastic resonance and stochastic resonance in a broad sense under the condition of Routh-Hurwitz stability. In addition, the stochastic resonance can be weakened as the memory time increases. Moreover, the numerical results of power spectrum of system are in agreement with the analytic results.