A pair of coupled erbium doped fiber ring lasers is used to explore thedynamics of coupled spatiotemporal systems. The lasers are mutually coupledwith a coupling delay less than the cavity round-trip time. We studysynchronization between the two lasers in the experiment and in a delaydifferential equation model of the system. Because the lasers are internallyperturbed by spontaneous emission, we include a noise source in the model toobtain stochastic realizations of the deterministic equations. Both amplitudesynchronization and phase synchronization are considered. We use the Hilberttransform to define the phase variable and compute phase synchronization. Wefind that synchronization increases with coupling strength in the experimentand the model. When the time series from two lasers are time-shifted in eitherdirection by the delay time, approximately equal synchronization is frequentlyobserved, so that a clear leader and follower cannot be identified. We definean algorithm to determine which laser leads the other when the synchronizationis sufficiently different with one direction of time shift, and statistics ofswitches in leader and follower are studied. The frequency of switching betweenleader and follower increases with coupling strength, as might be expectedsince the lasers mutually influence each other more effectively with strongercoupling.
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