Stability analysis of a noise-induced Hopf bifurcation

K. Mallick and P. Marcq ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2003, vol. 36, issue 1, 119-128

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

Date: 2003
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DOI: 10.1140/epjb/e2003-00324-y

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