Study of the Duffing–Rayleigh oscillator subject to harmonic and stochastic excitations by path integration

In this paper, the Duffing–Rayleigh oscillator subject to harmonic and stochastic excitations is investigated via path integration based on the Gauss–Legendre integration formula. The method can successfully capture the steady state periodic solution of probability density function. This path integr...

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Bibliographic Details
Published in:Applied mathematics and computation 2006-01, Vol.172 (2), p.1212-1224
Main Authors: Xie, W.X., Xu, W., Cai, L.
Format: Article
Language:English
Subjects:
Distribution theory
Duffing–Rayleigh oscillator
Exact sciences and technology
Harmonic and stochastic excitations
Mathematical analysis
Mathematics
Measure and integration
Partial differential equations
Path integration
Probability and statistics
Probability density
Probability theory and stochastic processes
Sciences and techniques of general use
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Summary:In this paper, the Duffing–Rayleigh oscillator subject to harmonic and stochastic excitations is investigated via path integration based on the Gauss–Legendre integration formula. The method can successfully capture the steady state periodic solution of probability density function. This path integration method, using the periodicity of the coefficient of associated Fokker–Planck–Kolmogorov equation, is extended to deal with the averaged stationary probability density, and is efficient to computation. Meanwhile, the changes of probability density caused by the intensities of harmonic and stochastic excitations, are discussed in three cases through the instantaneous probability density and the averaged stationary probability density.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2005.03.018