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Journal of Statistical Physics

, Volume 50, Issue 5–6, pp 897–912 | Cite as

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

  • Tamás Tél
Articles

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).

Key words

Stationary distribution weak noise expansion Hopf bifurcation van der Pol oscillator 

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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Tamás Tél
    • 1
  1. 1.Institute for Theoretical PhysicsEötvös UniversityBudapestHungary

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