Dynamical Characterization of Complex Heterogeneous Networks: Synchronization and Beyond

几个真实的社会、生物和技术系统可以被描述为一组通过连接连接起来的单独组件或节点，以形成一个“网络”。如果这些网络的特征是具有不同个体属性的节点和连接，则这些网络被表示为异质。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。了解异质性是如何影响网络功能的，可能会增强我们设计复杂动态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。其中包括成群结队的车辆、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它们的动态行为。然而，异质节点和连接的作用还没有得到充分的研究。在这个项目中，PI将把同步作为一个动态过程来研究，在这个过程中，异类网络的节点在共同的时间演化中收敛。异质网络的动态行为也将被考虑在其他背景下，包括对由地面和空中飞行器组成的机器人网络的研究，以及智能电网和网络上主体交互的进化博弈论的研究。这项研究将通过明确考虑复杂系统的异质特征来影响现有的知识和理解，从而提供对这些系统的更详细的描述和对其潜在应用的更好的洞察。描述这些系统的动力学特性的低维方法将由描述网络的整体动力学及其稳定性的较少数量的方程组成。利用非线性动力学理论中的工具，分析了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类网络，并实时输出对其动态特征的分析。这将为研究本文所研究的社会、技术、物理和生物网络的其他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验的复杂异质网络的迷人的动力学特性、它们的独特特征以及本文讨论的发现对许多科学和工程领域的令人兴奋的影响。

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.