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. Analytical solutions for the autocorrelation function and the power spectrum have been found. The power spectrum has a 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.
Tsimring
L S
LS
Institute for Nonlinear Science, University of California-San Diego, La Jolla, California 92093-0402, USA.
Pikovsky
A
A
D008962:Models, Theoretical; D009622:Noise