CAREER: Rescue and Control of Complex Networks of Dynamical Systems: Nonlinear Dynamics Approaches and Applications to Biological and Physical Networks

研究人员将开发和应用数学和计算方法来预测补偿性、救助性扰动，这些扰动可以缓解扰动复杂网络中故障的传播。这项研究的动机是关于大型生物和物理网络组成部分的信息越来越多，这为解决由大规模网络动力学决定的紧迫问题创造了前所未有的机会。该项目将使用非线性动力学和复杂网络技术，并将通过五个具有广泛意义的互补组成部分来实施：(1)确定性和(2)随机方法的发展；(3)减轻扰动食物网网络中的灭绝级联；(4)恢复有缺陷的新陈代谢网络中丢失的细胞功能；(5)控制电网中的级联故障。这项研究将导致识别物理上可实现的补偿性扰动，从而能够控制网络的大规模动态。该项目的总体目标是将这项研究的基本原则整合到三个不同框架内的教学和推广创新的开发中：(I)针对来自代表性不足群体的本科生的暑期实习活动；(Ii)用于本科生和研究生复杂系统教育的基于计算机的互动工具；以及(Iii)与芝加哥科学与工业博物馆合作的在线展览，这将进一步整合该项目的研究和教育成果。拟议的数学发展将创造可用于拯救和控制广泛领域的复杂网络的方法。这将使人们能够发现和描述可能促进在各种背景下取得突破的新现象。特别是，它将使新的生态系统管理方法能够阻止生物多样性的丧失，产生恢复丧失的细胞功能的新方法，对医学研究具有影响，并导致减少电网连锁故障的新方法。计划中的活动是跨学科的，将以传统学科研究项目无法提供的方式，为研究生和本科生(包括来自代表性不足群体的学生)提供一个独特的培训场所。教育和推广活动将有助于为西北大学的复杂系统教育建立基础设施，并将向广大和不同的受众传播研究成果和方法。

The investigator will develop and apply mathematical and computational methods to predict compensatory, rescue perturbations that can mitigate the propagation of failures in perturbed complex networks. The research is motivated by the increasing availability of information about the component parts of large biological and physical networks, which is creating an unprecedented opportunity to address pressing problems determined by large-scale network dynamics. The project will use nonlinear dynamics and complex network techniques and will be implemented through five complementary components of broad significance: the development of (1) deterministic and (2) stochastic methods to identify rescues; the application of these methods to (3) mitigate extinction cascades in perturbed food-web networks, (4) recover lost cellular function in defective metabolic networks, and (5) control cascading failures in power-grid networks. This research will lead to the identification of physically implementable compensatory perturbations, thereby enabling control of the network's large-scale dynamics. An overarching objective of the project is to integrate underlying principles of this research into the development of teaching and outreach innovations in three different frameworks: (i) summer internship activities for undergraduate students from underrepresented groups; (ii) computer-based interactive tools for undergraduate and graduate complex systems education; and (iii) on-line exhibits in partnership with Chicago's Museum of Science and Industry, which will further integrate the research and educational outcomes of this project.The proposed mathematical development will create methods that can be used to rescue and control complex networks in a wide range of domains. This will allow the discovery and characterization of new phenomena that are likely to foster breakthroughs in various contexts. In particular, it will enable new ecosystems management approaches to halt the loss of biodiversity, yield new methods to recover lost cellular function, with implications for medical research, and lead to novel methods to mitigate cascading failures in electrical power grids. The planned activities are interdisciplinary and will provide a unique training ground for graduate and undergraduate students (including students from underrepresented groups) in a way that traditional disciplinary research programs cannot. The educational and outreach activities will help create infrastructure for complex systems education at Northwestern and will disseminate the research results and methodologies to a large and diverse audience.