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

Research output: Contribution to journalArticle

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 1988

Fingerprint

noise intensity
Bifurcation Point
Stationary Distribution
Damping
damping
oscillators
Van Der Pol Oscillator
Rescaling
Coefficient
coefficients
Damped
Hopf Bifurcation
Bifurcation
expansion
Class

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

On the stationary distribution of self-sustained oscillators around bifurcation points. / Tél, T.

In: Journal of Statistical Physics, Vol. 50, No. 5-6, 03.1988, p. 897-912.

Research output: Contribution to journalArticle

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