Open AccessResonant behavior of a fractional linear oscillator with fluctuating frequency and periodically modulated noise
Author(s) -
Zhe Tu,
Hao Peng,
Wang Fei,
Hong Ma
Publication year - 2013
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.62.030502
Subject(s) - physics , laplace transform , parametric oscillator , amplitude , noise (video) , stochastic resonance , parametric statistics , excitation , mathematical analysis , mathematics , quantum mechanics , computer science , statistics , artificial intelligence , image (mathematics)
The resonant behavior of a fractional linear oscillator subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise is considered. Using Laplace transformation technique and Shapiro-Loginov formula, exact expressions of the first moment for the system response and its long-time amplitude are presented. The influence of the system parameters on the long-time behavior of the system response is discussed, such as fractional order, friction coefficient, driving frequency, noise intensity and relevant rate. It is found that the long-time amplitude of the fractional oscillator behaves non-monotonical, that is, there exist stochastic resonances in a wide sense. Moreover, generalized stochastic resonance with two peaks can be found subject to some appropriate parameters.