https://doi.org/10.1140/epjb/e2003-00324-y
Stability analysis of a noise-induced Hopf bifurcation
1
Service de Physique Théorique, Centre d'Études de Saclay,
91191 Gif-sur-Yvette Cedex, France
2
Institut de Recherche sur les Phénomènes Hors Équilibre,
Université de Provence,
49 rue Joliot-Curie, BP 146, 13384 Marseille Cedex 13, France
Corresponding author: a marcq@irphe.univ-mrs.fr
Received:
4
June
2003
Revised:
8
August
2003
Published online:
19
November
2003
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.
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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003
