DynSyst_Special_Topics: Time-varying dynamical networks: theory and applications

DynSyst_Special_Topics：时变动态网络：理论与应用

• 批准号: 1009744
• 负责人: Igor Belykh
• 金额: $ 20.63万
• 依托单位: Georgia State University Research Foundation, Inc.
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1009744&HistoricalAwards=false
• 关键词: DynSyst_Special_Topics; Time; varying; dynamical; networks

The research objective of this proposal is to investigate the influence of network structure on the dynamics and the information processing capabilities of networks with a time-varying coupling. This proposal focuses on a largely unexplored area, namely, mathematical analysis and modeling of networks that are composed of dynamical systems, whose coupling structure evolves over time, on a time scale that ranges from fast to slow. The development of the general rigorous theory of dynamical networks with on-off connections and its application to three specific types of engineering, ecological, and neuronal networks constitute the research component of the proposal. The first type is a class of stochastically switched engineering networks, such as power converters, communication and information processing networks with fast on-off connections. The second type of networks is interconnected ecological metapopulations, under the realistic assumption that the migration among the patches is sporadic and due to rare and short term meteorological conditions. The third type of networks is neuronal networks with time-varying connections. Research funded under this grant integrates knowledge from different disciplinary areas in applied mathematics and engineering, including stability and bifurcation theory, graph theory, information theory, ergodic theory and averaging.In many biological, ecological and engineering networks the coupling strength and the connection topology can vary in time. The proposed research applies rigorous mathematical techniques to investigate the interplay between time-varying network structure and overall network dynamics, in view of the time-varying network's use in information processing and its role in synchronization and pattern formation. In particular, the project investigates how the addition of fast switching connections can enhance the performance of networks with static links. The project also addresses the question of vulnerability of networks. Specifically, how well can networks process information when part of the individual systems or links are destroyed, and what advantages do time-varying networks of dynamical systems have over networks with static structure. The results will help to better understand the functioning of realistic networks in nature, as well as give general guidelines for designing information processing networks in engineering. The proposed research integrates research activities into the undergraduate and graduate curriculum through developing an interdisciplinary graduate course in the field of dynamical networks and mentoring undergraduate research projects. The grant directly supports one graduate and two undergraduate students, including those from under-represented groups.

该方案的研究目标是研究网络结构对时变耦合网络的动力学和信息处理能力的影响。这一建议侧重于一个基本上未被探索的领域，即对由动力系统组成的网络进行数学分析和建模，其耦合结构随着时间的推移而演变，时间尺度从快到慢不等。具有开关连接的动态网络的一般严格理论的发展及其在三种特定类型的工程网络、生态网络和神经网络中的应用构成了该提案的研究组成部分。第一类是一类随机开关工程网络，如具有快速开关连接的功率变换、通信和信息处理网络。第二种类型的网络是相互关联的生态集合种群，其现实假设是斑块之间的迁移是零星的，并且是由于罕见和短期的气象条件。第三类网络是具有时变连接的神经元网络。这笔拨款资助的研究综合了应用数学和工程中不同学科领域的知识，包括稳定性和分叉理论、图论、信息论、遍历理论和平均。在许多生物、生态和工程网络中，耦合强度和连接拓扑可以随时间变化。鉴于时变网络在信息处理中的应用及其在同步和模式形成中的作用，本研究采用严格的数学技术来研究时变网络结构和整体网络动力学之间的相互作用。特别是，该项目调查了添加快速交换连接如何提高具有静态链路的网络的性能。该项目还解决了网络的脆弱性问题。具体地说，当个别系统或链路的一部分被破坏时，网络处理信息的能力如何，以及动态系统的时变网络相对于静态结构的网络有什么优势。这些结果将有助于更好地理解现实网络在自然界中的功能，并为工程中信息处理网络的设计提供一般指导。拟议的研究通过开发动态网络领域的跨学科研究生课程和指导本科生研究项目，将研究活动纳入本科生和研究生课程。该助学金直接资助一名研究生和两名本科生，包括来自代表性不足群体的学生。