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Noise-induced reentrant transition of the stochastic Duffing oscillator

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Abstract.

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.

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Authors and Affiliations

  1. Service de Physique Théorique, Centre d’Études de Saclay, 91191, Gif-sur-Yvette Cedex, France

    K. Mallick

  2. Institut de Recherche sur les Phénoménes Hors Équilibre, Université de Provence, 49 rue Joliot-Curie, BP 146, 13384, Marseille Cedex 13, France

    P. Marcq

Authors
  1. K. Mallick
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  2. P. Marcq
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Correspondence to P. Marcq.

Additional information

Received: 20 February 2004, Published online: 20 April 2004

PACS:

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.) - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems

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Mallick, K., Marcq, P. Noise-induced reentrant transition of the stochastic Duffing oscillator. Eur. Phys. J. B 38, 99–102 (2004). https://doi.org/10.1140/epjb/e2004-00104-3

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  • DOI: https://doi.org/10.1140/epjb/e2004-00104-3

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