BECS: Collaborative Research: Dynamical Networks and Collective Synchronization of Coupled Lasers

该奖项的研究目标是对互连动力系统的复杂网络进行严格的数学分析，并将开发的方法应用于控制和集体同步耦合半导体激光器阵列。其主要思想是基于动态的，而不是传统的静态的，网络的拓扑结构的描述，它允许考虑的分析和评估的累积行动的所有三个主要成分，形成一个动态网络：1。网络元素的局部动态，2。网络元素之间的相互作用，3。网络的拓扑结构。该项目旨在将数学基础与真实的世界应用相结合，开发的数学机器将用于寻找同步条件和选择耦合半导体激光器阵列同步的控制参数。该项目将推动复杂动力学网络、非线性动力学和耦合半导体激光器领域的发展。为半导体激光器在空间、光纤、水下通信、焊接、切割等应用中可能产生重大技术影响的激光实验提供理论指导。该项目通过本科和研究生教育和研究培训，短期课程和研讨会的发展，以及K-12教育的推广，将研究项目与教育活动相结合。 该团队还计划招募女性工程专业学生，并将她们留在科学和工程领域。

The research objective of this award is to conduct rigorous mathematical analysis of complex networks of interconnected dynamical systems, and apply the developed methods to control and collectively synchronize arrays of coupled semiconductor lasers. The main idea is based on the dynamical, rather than traditional static, description of the topology of a network, which allows to account for an analysis and evaluation of cumulative action of all three major ingredients that form a dynamical network: 1. local dynamics of elements of the network, 2. interactions between the elements of a network, 3. topology of the network. The project seeks an integration of the mathematical foundations with real world applications, and the developed mathematical machinery will be used to find synchronization conditions and to choose control parameters for synchronization of arrays of coupled semiconductor lasers.The project will advance the fields of complex dynamical networks, nonlinear dynamics, and coupled semiconductor lasers, and provide theoretical guidance for laser experiments that may lead to significant technological impact in applications of semiconductor lasers such as space, fiber, and underwater communication, welding, cutting and others. The project integrates research projects with education activities through undergraduate and graduate education and research training, short course and workshop development, and outreach to K-12 education. The team also plans to recruit women engineering students and to retain them into careers in science and engineering.