Synchronization of chaotic systems: Feedback, mutual interaction and unidirectional coupling with delay

从理论上探讨由时滞耦合相互作用的混沌系统的性质。特别是，混沌同步将研究不同类型的耦合和拓扑。相互作用和定向耦合之间的区别将是这个项目的主要焦点。迭代映射的解析计算将支持具有延迟的混沌微分方程的数值模拟。该项目与混沌半导体激光器的实验密切合作。因此，该项目的数值研究将集中在具有反馈的半导体激光器的速率方程上。该项目的最终目标是找到通过公共通道传输秘密消息的新方法。因此，激光网络和混沌通滤波器从混沌激光束中恢复信息将是这一理论研究的主要部分。

The properties of chaotic systems interacting by time-delayed couplings will be explored theoretically. In particular, chaos synchronization will be investigated for different types of couplings and topologies. The difference between mutual interaction and directed couplings will be the main focus of this project. Numerical simulations of chaotic differential equations with delay will be supported by analytical calculations of iterated maps. This project is running in close collaboration with experiments on chaotic semiconductor lasers. Therefore, the numerical investigations of the project will concentrate on the rate equations for semiconductor lasers with feedback. The final goal of the project is to find novel methods to transmit secret messages over public channels. Hence, networks of lasers and chaos pass filter to recover the messages from chaotic laser beams will be a main part of this theoretical investigation.