Network of chaotic units: Sychronization with time-delayed coupling

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A network of chaotic units can synchronize: All units relax to a common chaotic trajectory. This counterintuitive phenomenon is recently discussed in the context of cooperative behavior of arrays of electronic circuits and lasers, but it also has implications on neurobiology and secure communication.In this proposal, networks with time-delayed transmission of coupling signals between the chaotic units are investigated. Analytical and numerical calculations should give the conditions under which complete synchronization without time-shift is possible, although the couplings have long time delay. In particular the competition between different time scales will be studied.The second part of this project will concentrate on the conditions on possible secure communication with chaotic semiconductor lasers. Mechanisms should be developed and investigated by which an array of chaotic elements can synchronize while a third unit, recording the transmission, is not able to synchronize.This project will continue the close collaboration with an experimental group of the Bar Illan University working on chaotic semiconductor lasers.