Noise-induced reentrant transition of the stochastic Duffing oscillator of the stochastic Duffing oscillator

Kirone Mallick (1) , Philippe Marcq (2)

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

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.

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

Kirone Mallick, Philippe Marcq. Noise-induced reentrant transition of the stochastic Duffing oscillator of the stochastic Duffing oscillator. The European Physical Journal B: Condensed Matter and Complex Systems, 2004, 38, n° 1, pp.99 - 102. ⟨10.1140/epjb/e2004-00104-3⟩. ⟨hal-00014887⟩