https://doi.org/10.1140/epjb/e2006-00089-9
Stability of a nonlinear oscillator with random damping
1
Laboratoire de Physique Statistique de l'ENS, 24 rue Lhomond, 75231 Parix Cedex 05, France
2
Service de Physique Théorique, CEA Saclay, 91191 Gif sur Yvette Cedex, France
Corresponding author: a n.leprovost@sheffield.ac.uk
Received:
24
October
2005
Revised:
10
January
2006
Published online:
31
March
2006
A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be predicted from the analysis of the moments of the linearized equation. In the case of a white noise, an exact formula for the Lyapunov exponent of the system is derived. We then calculate the critical damping for which the nonlinear system becomes unstable. We also characterize the intermittent structure of the bifurcated state above threshold and address the effect of temporal correlations of the noise by considering an Ornstein-Uhlenbeck noise.
PACS: 02.50.-r – Probability theory, stochastic processes and statistics (see also section 05 Statistical physics, thermodynamics, and nonlinear dynamical systems) / 05.40.-a – Fluctuation phenomena, random process, noise and Brownian motion / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006
