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.

几种真实的社会，生物学和技术系统可以描述为通过连接形成“网络”的单个组件或节点的集合。如果这些网络的特征在于具有不同单个属性的节点和连接，则将这些网络表示为异质。异质性是许多自然网络的典型特征。例如，神经元网络的特征是不同类型的神经元及其之间的连接。 了解异质性如何影响网络功能可能会增强我们设计和与复杂的动力学系统相互作用的能力，这些动力系统可以描述为各种技术应用中发现的网络。其中包括大量的车辆，机器人，智能电网。大量文献研究了这些网络的结构如何影响其动态行为。但是，尚未对异质淋巴结和连接的作用进行全面研究。 在该项目中，PI将研究同步作为动态过程，在这种过程中，异质网络的节点在常用时间演变中收敛。在其他情况下，还将考虑异质网络的动态行为，包括研究由地面和航空车组成的机器人网络，以及针对网络交互的智能网格和进化游戏理论。这项研究将影响当前的知识并通过明确考虑其异质特征来理解复杂系统，这反过来将提供对这些系统的更详细的特征，并更好地了解其潜在应用。对这些系统动力学表征的表征的低维方法将包括描述网络总体动力学及其稳定性的方程数量。将采用非线性动力学理论的工具来分析所考虑的网络中固定点，极限周期和混乱动态的出现条件。此外，还将开发一个简单而直观的在线小程序，该小程序将允许用户上传给定的异构网络，并将实时输出对其动态功能的分析。这将为与此处研究的社会，技术，物理和生物网络一起工作的其他研究人员提供宝贵的工具。该小程序还将用于使更广泛的受众了解本研究中检查的复杂异质网络的引人入胜的动力学特性，其独特的特征，以及本文讨论的发现的令人兴奋的含义，以了解许多科学和工程领域。