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  • nonlinear systems  (1)
  • Springer  (1)
  • 1
    ISSN: 1573-269X
    Keywords: nonlinear systems ; Fokker–Planck equation ; Galerkin procedure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, nonlinear stochastic systems are investigatedvia associated Fokker–Planck equations. Their stationary solutions arecalculated by expansions into orthogonal functions, e.g. especiallyadjusted polynomials and Fourier series. The weighting functions of thenew polynomials are obtained by the application of the stochasticaveraging method. The proposed analysis is demonstrated with severalexamples. The first one is a two-dimensional problem of nonlinearoscillators driven by white noise. The second one describes two-massoscillators with independent coloured noise excitations leading tosix-dimensional probability density functions. The next example ispresenting a system driven by both harmonic and stochastic excitationleading to three-dimensional probability density functions. Finally,oscillators with dry friction characteristics are examined.
    Type of Medium: Electronic Resource
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