Stability analysis of a noise-induced Hopf bifurcation |
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Authors: | K?Mallick Email author" target="_blank">P?MarcqEmail author |
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Institution: | (1) Service de Physique Théorique, Centre dÉtudes de Saclay, 91191 Gif-sur-Yvette Cedex, France;(2) Institut de Recherche sur les Phénoménes Hors Équilibre, Université de Provence, 49 rue Joliot-Curie, BP 146, 13384 Marseille Cedex 13, France |
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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 oscillators mean energy, is studied both close to and far from the bifurcation.Received: 8 August 2003, Published online: 19 November 2003PACS:
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 |
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