2001/07/06 by Lev S. Tsimring, L. S. Tsimring, Arkady Pikovsky +1 · 2 citations
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physrevlett.87.250602
4 pages, 4 figures, submitted to Physical Review Letters
arxiv created 2001/07/06 · openalex publication_date 2001/11/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.