2006/03/01 by Leah B. Shaw, L. B. Shaw, I. B. Schwartz +5 · 2 citations
Agricultural and Biological Sciences · Computer Science · Physics and Astronomy · #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation #Plant and animal studies #nlin.CD
paper · pdf · doi:10.1063/1.2150407
To appear in CHAOS
openalex publication_date 2006/03/01 · arxiv created 2006/03/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A pair of coupled erbium doped fiber ring lasers is used to explore the dynamics of coupled spatiotemporal systems. The lasers are mutually coupled with a coupling delay less than the cavity round-trip time. We study synchronization between the two lasers in the experiment and in a delay differential equation model of the system. Because the lasers are internally perturbed by spontaneous emission, we include a noise source in the model to obtain stochastic realizations of the deterministic equations. Both amplitude synchronization and phase synchronization are considered. We use the Hilbert transform to define the phase variable and compute phase synchronization. We find that synchronization increases with coupling strength in the experiment and the model. When the time series from two lasers are time shifted in either direction by the delay time, approximately equal synchronization is frequently observed, so that a clear leader and follower cannot be identified. We define an algorithm to determine which laser leads the other when the synchronization is sufficiently different with one direction of time shift, and statistics of switches in leader and follower are studied. The frequency of switching between leader and follower increases with coupling strength, as might be expected since the lasers mutually influence each other more effectively with stronger coupling.