Stability analysis of a noise-induced Hopf bifurcation

Details Stability analysis of a noise-induced Hopf bifurcation Stability analysis of a noise-induced Hopf bifurcation

2003-12-15

arxiv.org/abs/cond-mat/0312360v1

Eur. Phys. J. B, Vol 36 (2003) 119

Physics

Condensed Matter

Statistical Mechanics

10 pages, 8 figures

Scientific paper

10.1140/epjb/e2003-00324-y

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.

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