复合聚类网络同步能力的尺度可变性及其粗粒化方法研究

The structure and scale of real complex networks are evolutionary, such as Internet and WWW, whose sizes are continuously increasing. But as the networks grow, how their dynamics change and whether their synchronizing capacity can keep the same or change to what?Answering these questions is very important to understand, design and control the functions of real systems, and it has wide applications in biology networks, computer networks and social network. Our project focuses on the problems of the scale variability of synchronizability in a class of compound clustered networks. In view of the Laplacian spectral of a unified sub-network, we use the multilayer and self-similar nested manner to construct the model of compound clustered networks. Employing the theories of complex network and dynamic system, and the master stability function approach, we investigate the evolution rules of synchronizability as the network sizes increase, and thus obtain the conclusions about the scale variability of synchronizability and vulnerability on the compound clustered networks. Further, we design different schemes for coarse graining process to deal with the compound clustered network with large scale, and by comparing the synchronizing capacity of the coarse-graining networks, we gain the better one to keep the network synchronizability. The results can provide new methods and ideas for the research and application of dynamics of large-scale complex system in real world.

现实复杂网络的结构和规模是演化的，像Internet, WWW等都在不断地增大。当网络规模越来越大，网络的动力学会发生怎样变化？网络的同步能力是否能保持或如何变化？这些问题的研究对于复杂系统功能的理解、设计与控制都至关重要，在生物网络、计算机网络、社会网络中都有着广泛的应用背景。本项目重点研究一类复合聚类网络同步能力的尺度可变性问题。以归一化子网络的Laplacian矩阵特征值谱为切入点，以多层次自相似嵌套方式构造复合聚类网络模型，综合运用复杂网络、动力系统理论及主稳定函数方法，探索网络同步性能随网络规模尺度的变化规律，最终获得复合聚类网络的同步能力与脆弱性的尺度可变性结论。进一步设计不同的粗粒化模块凝聚方案，对大尺度复合聚类网络进行粗粒化提取，通过比较不同粗粒化网络的同步能力，获得较优的保持网络同步能力的粗粒化方案，为现实大规模复杂系统的动力学研究与应用提供新的方法和思路。

现实复杂系统的结构和功能是不断演化的，当网络的规模越来越大时其动力学会发生怎样变化？网络的同步能力是否能保持或如何变化？这些问题的研究对于复杂系统功能的理解、设计与控制都至关重要，在生物网络、计算机网络、社会网络中都有着广泛的应用背景。本项目重点研究了复合聚类（多层）网络同步能力的尺度可变性和大规模网络的粗粒化方法。以一般网络的Laplacian矩阵和多层网络的超Laplacian矩阵的特征值谱为切入点，综合运用复杂网络、动力系统理论及主稳定函数方法，研究了网络同步性能随网络规模尺度和结构参数的变化规律，获得了复合聚类（多层）网络的同步能力随网络规模和结构变化的可变性结论。对于大规模复杂网络提出了多种不同的粗粒化方案，通过比较不同粗粒化网络的同步能力，获得较优的保持网络同步能力的粗粒化方案，进一步提出了网络粗粒化优化的概念及算法。本项目的研究丰富了复杂网络粗粒化的研究内容和方法，为现实大规模复杂系统的设计与控制提供新方法和新思路。