Dynamical Characterization of Complex Heterogeneous Networks: Synchronization and Beyond

复杂异构网络的动态表征：同步及其他

• 批准号: 1400193
• 负责人: Francesco Sorrentino
• 金额: $ 28.99万
• 依托单位: University of New Mexico
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1400193&HistoricalAwards=false
• 关键词: Dynamical; Characterization; Complex; Heterogeneous; Networks

Several real social, biological, and technological systems can be described as sets of individual components or nodes coupled by connections to form a "network." These networks are denoted as heterogeneous if they are characterized by nodes and connections with different individual properties. Heterogeneity is typical of many natural networks; for example, neuronal networks are characterized by different types of neurons and connections between them. Understanding how heterogeneity affects the network functions may enhance our ability to design and interact with complex dynamical systems that can be described as networks as found in various technological applications. These include swarms of vehicles, robots, smart grids among others. A large body of literature has studied how the structure of these networks affects their dynamic behavior. However, the role of heterogeneous nodes and connections has not been fully investigated. In this project, the PI will investigate synchronization as a dynamic process where the nodes of heterogeneous networks converge on a common time evolution. The dynamic behavior of heterogeneous networks will also be considered in other contexts, including the study of robotic networks composed of ground and aerial vehicles, as well as smart grids and evolutionary game theory for agents interacting over a network.This research will impact the current knowledge and understanding of complex systems by explicitly taking into account their heterogeneous features, which in turn will provide a more detailed characterization of these systems and a better insight into their potential applications. A low dimensional approach to the characterization of the dynamics of these systems will consist of a reduced number of equations that describe the overall dynamics of the network and its stability. Tools from the theory of nonlinear dynamics will be employed to analyze the conditions for the emergence of fixed points, limit cycles and chaotic dynamics in the networks under consideration. In addition, a simple and intuitive online applet will be developed that will allow users to upload a given heterogeneous network and will output an analysis of its dynamical features in real time. This will provide a valuable tool to other researchers who work with social, technological, physical, and biological networks of the kind investigated herein. The applet will also be used to expose a broader audience to the fascinating dynamical properties of the complex heterogeneous networks examined in this study, to their unique characteristics, and to the exciting implications of the findings discussed herein for a number of scientific and engineering fields.

一些真实的社会、生物和技术系统可以被描述为通过连接耦合形成“网络”的各个组件或节点的集合。如果这些网络的特征在于节点和连接具有不同的个体属性，则它们被称为异构网络。异质性是许多自然网络的典型特征。例如，神经元网络的特征在于不同类型的神经元以及它们之间的连接。 了解异质性如何影响网络功能可能会增强我们设计复杂动力系统并与之交互的能力，这些系统可以被描述为各种技术应用中的网络。其中包括大量车辆、机器人、智能电网等。大量文献研究了这些网络的结构如何影响其动态行为。然而，异构节点和连接的作用尚未得到充分研究。 在这个项目中，PI 将研究同步作为一个动态过程，其中异构网络的节点汇聚在一个共同的时间演化上。异构网络的动态行为也将在其他背景下得到考虑，包括研究由地面和空中车辆组成的机器人网络，以及智能电网和网络交互的进化博弈论。这项研究将通过明确考虑复杂系统的异构特征来影响当前对复杂系统的知识和理解，这反过来又将为这些系统提供更详细的表征，并更好地洞察其潜在应用。表征这些系统动力学的低维方法将由减少数量的方程组成，这些方程描述网络的整体动力学及其稳定性。将采用非线性动力学理论的工具来分析所考虑的网络中出现不动点、极限环和混沌动力学的条件。此外，还将开发一个简单直观的在线小程序，允许用户上传给定的异构网络，并实时输出其动态特征的分析。这将为其他研究本文所研究的社会、技术、物理和生物网络的研究人员提供一个有价值的工具。该小程序还将用于向更广泛的受众展示本研究中检查的复杂异构网络的迷人动态特性、其独特的特征以及本文讨论的研究结果对许多科学和工程领域的令人兴奋的影响。