Noise-induced reentrant transition of the stochastic Duffing oscillator

  • K. Mallick
  • P. MarcqEmail author


We derive the exact bifurcation diagram of the Duffing oscillator with parametric noise thanks to the analytical study of the associated Lyapunov exponent. When the fixed point is unstable for the underlying deterministic dynamics, we show that the system undergoes a noise-induced reentrant transition in a given range of parameters. The fixed point is stabilised when the amplitude of the noise belongs to a well-defined interval. Noisy oscillations are found outside that range, i.e., for both weaker and stronger noise.


Analytical Study Lyapunov Exponent Bifurcation Diagram Parametric Noise Duffing Oscillator 
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© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Service de Physique ThéoriqueCentre d’Études de SaclayGif-sur-Yvette CedexFrance
  2. 2.Institut de Recherche sur les Phénoménes Hors ÉquilibreUniversité de ProvenceMarseille Cedex 13France

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