" Synchronization of mutually coupled systems in the presence of long delays "

Dr.  Alexandra Landsman

Abstract

   Complete chaotic synchronization of end lasers has been observed  in a line of mutually coupled, time-delayed system of three lasers.  As mentioned in the October 6 issue of Science (vol. 314, p. 37), this experiment has significance to synchronization of other nonlinear systems with long delays, where it has been proposed by Singer and colleagues that a similar mechanism may be at work behind the observed synchronization of the opposite hemispheres of the brain.  Time delays significantly complicate the analysis, and the mechanism behind the synchronization has so far not been elucidated.  The present work uses ideas from generalized synchronization to explain chaotic synchronization in the presence of long delays.  As an example, the three laser system is analyzed, using stability analysis close to the synchronization manifold.  The results explain and predict the dependence of synchronization on various parameters, such as  time-delays, strength of coupling, and dissipation.  One interesting and counter-intuitive result of the analysis is that increasing the delay actually improves synchronization.  The analyticly based predictions agree with numerical results.