https://doi.org/10.1140/epjb/e2004-00104-3
Noise-induced reentrant transition of the stochastic Duffing oscillator
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:
2
December
2003
Revised:
20
February
2004
Published online:
20
April
2004
We derive the exact bifurcation diagram of the Duffing oscillator with parametric noise thanks to the analytical study of the associated Lyapunov exponent. When the fixed point is unstable for the underlying deterministic dynamics, we show that the system undergoes a noise-induced reentrant transition in a given range of parameters. The fixed point is stabilised when the amplitude of the noise belongs to a well-defined interval. Noisy oscillations are found outside that range, i.e., for both weaker and stronger noise.
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, 2004
