The van Kampen expansion for the Fokker-Planck equation of a duffing oscillator

Edward M. Weinstein, Haym Benaroya

Research output: Contribution to journalArticle

11 Scopus citations


In Rodríguez and van Kampen's 1976 paper a method of extracting information from the Fokker-Planck equation without having to solve the equation is outlined. The Fokker-Planck equation for a Duffing oscillator excited by white noise is expanded about the intensity α of the forcing function. This expansion is carried to order {Mathematical expression}. However, no studies are made of the effects of the order of the expansion or variation of the parameters, nor are comparisons made to experimental results. In the present paper, the expansion is carried to a higher order, {Mathematical expression}, results are presented and compared to Monte Carlo experiments using both white and colored noise, and parametric studies are performed on the intensity of the forcing function and the damping coefficient. It is found that the expansion method works well for the case of white noise and for colored noise where the correlation time is less than 0.1 sec, but fails to give certain details. It is also found that the system behaves as expected when the parameters are varied.

Original languageEnglish (US)
Pages (from-to)667-679
Number of pages13
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - Nov 1 1994

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Duffing oscillator
  • Fokker-Planck equation
  • Monte Carlo
  • colored noise
  • van Kampen expansion
  • white noise

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