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Open Access item Derivation of amplitude equations for nonlinear oscillators subject to arbitrary forcing

Authors:Mayol, Catalina
Toral, Raúl
Mirasso, Claudio R.
Keywords:[PACS] Stochastic analysis methods (Fokker-Planck, Langevin, etc.), [PACS] Function theory, Analysis: Approximations and expansions, [PACS] Noise
Issue Date:24-Jun-2004
Citation:Physical Review E 69, 066141 (1-6) (2004)
Abstract:By using a generalization of the multiple scales technique we develop a method to derive amplitude equations for zero-dimensional forced systems. The method allows to consider either additive or multiplicative forcing terms and can be straightforwardly applied to the case that the forcing is white noise. We give examples of the use of this method to the case of the van der Pol–Duffing oscillator. The writing of the amplitude equations in terms of a Lyapunov potential allow us to obtain an analytical expression for the probability distribution function which reproduces reasonably well the numerical simulation results.
Description:6 pages.-- PACS nrs.: 05.10.Gg, 02.30.Mv, 05.40.Ca.-- ArXiv pre-print available at: http://arxiv.org/abs/cond-mat/0312077v1.-- ©2004 The American Physical Society
Publisher version (URL):http://dx.doi.org/10.1103/PhysRevE.69.066141
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