Stability analysis of a noise-induced Hopf bifurcation

Kirone Mallick (1) , Philippe Marcq (2)

1 SPhT - Service de Physique Théorique
2 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre

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.

Domaines: Mécanique des fluides [physics.class-ph]

Kirone Mallick, Philippe Marcq. Stability analysis of a noise-induced Hopf bifurcation. The European Physical Journal B: Condensed Matter and Complex Systems, 2003, 36, pp.119 - 128. ⟨hal-00014829⟩