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CHAOS VOLUME 10 NUMBER 3 SEPTEMBER 2000 Experimental investigation of high quality synchronization of coupled oscillators Jonathan N Blakelya and Daniel J Gauthier Department of Physics and Center for Nonlinear and Complex Systems Duke University Box 90305 Durham North Carolina 27708 Gregg Johnson Thomas L Carroll and Louis M Pecora Code 6343 U S Naval Research Laboratory Washington DC 20375 Received 30 November 1999 accepted for publication 2 May 2000 We describe two experiments in which we investigate the synchronization of coupled periodic oscillators Each experimental system consists of two identical coupled electronic periodic oscillators that display bursts of desynchronization events similar to those observed previously in coupled chaotic systems We measure the degree of synchronization as a function of coupling strength In the first experiment high quality synchronization is achieved for all coupling strengths above a critical value In the second experiment no high quality synchronization is observed We compare our results to the predictions of the several proposed criteria for synchronization We find that none of the criteria accurately predict the range of coupling strengths over which high quality synchronization is observed 2000 American Institute of Physics S1054 1500 00 01203 9 noise is injected into the system For example Ali and Menzinger1 recently showed that a globally stable limit cycle oscillator subject to small amounts of noise can display an explosive divergence of trajectories away from the limit cycle The origin of this disproportionate response to small perturbations is the fact that the limit cycle is composed of segments of varying local stability most of which are stable but some of which are highly unstable as shown schematically in Fig 1 In regions of pronounced local instability a perturbation may undergo transient growth before decaying asymptotically A similar behavior is displayed by nonnormal linear systems as shown schematically

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