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Stability analysis of a noise-induced Hopf bifurcation

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  • K. Mallick
  • P. Marcq

Abstract

We study analytically and numerically the noise-induced transition between an absorbing and an oscillatory state in a Duffing oscillator subject to multiplicative, Gaussian white noise. We show in a non-perturbative manner that a stochastic bifurcation occurs when the Lyapunov exponent of the linearised system becomes positive. We deduce from a simple formula for the Lyapunov exponent the phase diagram of the stochastic Duffing oscillator. The behaviour of physical observables, such as the oscillator’s mean energy, is studied both close to and far from the bifurcation. Copyright Springer-Verlag Berlin/Heidelberg 2003

Suggested Citation

  • K. Mallick & P. Marcq, 2003. "Stability analysis of a noise-induced Hopf bifurcation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 36(1), pages 119-128, November.
    • Handle: RePEc:spr:eurphb:v:36:y:2003:i:1:p:119-128
    DOI: 10.1140/epjb/e2003-00324-y
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    Cited by:

    1. Bashkirtseva, Irina & Ryashko, Lev & Schurz, Henri, 2009. "Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 72-82.
    2. Ryashko, L. & Bashkirtseva, I. & Gubkin, A. & Stikhin, P., 2009. "Confidence tori in the analysis of stochastic 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 256-269.

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