Network of chaotic units: Sychronization with time-delayed coupling

混沌单元网络可以同步：所有单元松弛到一个共同的混沌轨迹。这种反直觉的现象最近在电子电路阵列和激光的合作行为的背景下进行了讨论，但它也对神经生物学和安全通信有影响。本文研究了混沌单元间耦合信号延时传输的网络。解析和数值计算应该给出在没有时移的情况下完全同步的条件，尽管耦合有很长的时间延迟。特别是不同时间尺度之间的竞争将被研究。该项目的第二部分将集中于混沌半导体激光器可能的安全通信条件。应该开发和研究一种机制，通过这种机制，一组混沌元素可以同步，而记录传输的第三个单元则不能同步。该项目将继续与巴伊兰大学的一个研究混沌半导体激光器的实验小组密切合作。

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.