29 research outputs found
Noise-induced dynamics in bistable systems with delay
Noise-induced dynamics of a prototypical bistable system with delayed
feedback is studied theoretically and numerically. For small noise and
magnitude of the feedback, the problem is reduced to the analysis of the
two-state model with transition rates depending on the earlier state of the
system. In this two-state approximation, we found analytical formulae for the
autocorrelation function, the power spectrum, and the linear response to a
periodic perturbation. They show very good agreement with direct numerical
simulations of the original Langevin equation. The power spectrum has a
pronounced peak at the frequency corresponding to the inverse delay time, whose
amplitude has a maximum at a certain noise level, thus demonstrating coherence
resonance. The linear response to the external periodic force also has maxima
at the frequencies corresponding to the inverse delay time and its harmonics.Comment: 4 pages, 4 figures, submitted to Physical Review Letter