On the stationary distribution of self-sustained oscillators around bifurcation points

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9 Citations (Scopus)

Abstract

A double expansion in powers of the damping coefficient and noise intensity is shown to be a powerful method for obtaining the stationary distribution of systems that after rescaling become weakly damped conservative ones. Systems undergoing Hopf bifurcations belong to this class. As an illustrative example, the generalized van der Pol oscillator is considered around its bifurcation point. A calculation is carried out up to third order in both the noise intensity and the bifurcation parameter (damping coefficient).

Original languageEnglish
Pages (from-to)897-912
Number of pages16
JournalJournal of Statistical Physics
Volume50
Issue number5-6
DOIs
Publication statusPublished - Mar 1 1988

Keywords

  • Hopf bifurcation
  • Stationary distribution
  • van der Pol oscillator
  • weak noise expansion

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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