Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-07-06
Physics
Condensed Matter
Statistical Mechanics
4 pages, 4 figures, submitted to Physical Review Letters
Scientific paper
10.1103/PhysRevLett.87.250602
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.
Pikovsky Arkady
Tsimring Lev S.
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