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

该奖项的研究目标是对相互关联的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。其主要思想是基于对网络拓扑的动态描述，而不是传统的静态描述，这允许对构成动态网络的所有三个主要成分的累积作用进行分析和评估：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。该项目寻求将数学基础与实际应用相结合，开发的数学机制将用于寻找耦合半导体激光器阵列同步的同步条件和选择控制参数。该项目将推进复杂动态网络、非线性动力学和耦合半导体激光器领域，并为激光实验提供理论指导，这些实验可能导致半导体激光器在空间、光纤和水下通信、焊接、切割等应用中产生重大技术影响。该项目通过本科生和研究生教育和研究培训、短期课程和讲习班的发展以及对K-12教育的推广，将研究项目与教育活动结合起来。该团队还计划招收工程专业的女性学生，并将她们留下来从事科学和工程领域的工作。

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.