基于特征值谱的有向社团网络的同步过程

项目名称： 基于特征值谱的有向社团网络的同步过程

项目编号： No.61304164

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 陈娟

作者单位： 武汉科技大学

项目金额： 23万元

中文摘要： 同步是复杂网络的研究主题之一。目前人们主要研究网络的同步条件及同步态的稳定性等，忽视了网络还没有完全同步时的信息。而同步过程刻画了复杂网络的中尺度演化机制，揭示了复杂网络的拓扑尺度，为研究复杂网络的社团发现与分层问题提供动力学上的方法。无向网络同步过程近几年开始研究，最新成果表明，随机网络，小世界网络与无标度网络的同步过程和同步方式有着本质的区别。但是有向网络的同步过程还没有涉及。网络边的有向性对网络的谱分布和同步过程有着重要影响。基于以上考虑，我们拟对以下几个问题展开研究：有向社团网络的Laplace谱的分布规律；有向社团网络的同步过程及失同步过程；有向社团网络的同步过程与特征值谱分布之间的关系；基于同步过程探测有向网络的社团结构。本项目的研究目的是理解有向边及社团在复杂网络动力学行为的发展和形成中发挥的特定作用，为优化有向网络同步提供新的理论和方法，也为复杂网络的中尺度研究提供新思路。

中文关键词： 复杂网络；社团网络；有向网络；特征值谱；同步过程

英文摘要： Synchronization is one of the hottest subjects of complex dynamical networks. Most of the present work focus on conditions to achieve synchronization, the stability of the fully synchronized state, without considering the information about what happens in the path to complete synchronization. Synchronization processes describe in detail the actual evolution mechanism of mesoscales in complex networks, reveal all different topological scales, and provide dynamical methods for the problem of the detection and hierarchy of communities. Researchers have begun to pay close attention to synchronization processes in undirected networks in recent years. The latest results uncover that processes and patterns of synchronization in random, small-world are far different form those in scale-free networks. However, there are few studies on synchronization processes in directed networks. We are concerned about how the directed property of edges in directed networks infulences the eigenvale spectra of coupling matrix and synchronization processes. Based on the above considerations, we plan to carry out our research from the following problems: the properties of Laplacian spectra of directed community networks; synchronization and desynchronization proocesses in directed community networks; the relationship between synchronizati

英文关键词： complex networks；community networks；directed networks；Laplacian spectra；synchronization processes