多层网络的动力学特性及结构分析

With the development of Internet age, the study of a single network does not meet our demand any more. To understand many phenomena in our daily life, we must go deep into the network of networks, which is also called multiplex network. Since rare literature and few methods can be found on this topic, it is necessary to introduce a suitable mathematical model to describe multiplex network. Using the theory on the relationship between dynamics and topology of single network, the properties of multiplex network can be analyzed. In view of the differences among layer, the following questions are focused on. First, what the dynamical relationship between multiplex network and every single layer is. Second, how does the importance of node changes with single networks merging into a multiplex network. Third, how to pin a multiplex network to the target based on the node importance of this network. Last, how to reconstruct the topology of multiplex network in consideration of the characteristic of real network. Through our research, new theoretical approaches and angles are expected for many fields, such as sociology, biology and Internet of things.

随着网络时代的发展，单一网络的研究已不能满足需求，必须深入到网络的网络，即多层网络。而这方面文献很少，理论方法和技术手段都很缺乏，因此有必要引入一个合适的数学模型来描述多层网络，并利用目前已取得的单层网络结构、动力学与特征值谱关系的理论和方法，对多层网络进行深入而细致的分析。本项目拟利用多层网络与单层网络特征值谱之间的紧密联系，充分考虑到分层结构的差异以及层间连接的复杂性，首先研究多层网络的动力学演化与单层结构和单层动力学之间的关系，不同的单层结构将如何影响多层网络整体动力学的演化；其次考察每层子网络的拓扑结构在多层网络节点重要性排序改变中所起的作用，并在此基础上牵制控制重要节点；最后结合实际网络特点，重塑多层网络的拓扑结构。本项目旨在按层研究多层网络的动力学性质和结构特点，为探索大规模网络的动力学演化机制及拓扑结构重塑等问题奠定基础，为社会学、生物学、物联网等众多学科提供新的视角和方法。

复杂网络在我们身边无处不在，一直是系统与控制学科的前沿和热点。因为单层网络是多层网络的基础和本质，本项目在相关问题对单层网络进一步探讨之后，深入到多层网络研究其各种理论、各种性质、各种现象的区别与联系。本项目在深入研究单层网络的同步规律、同步能力、结构辨识的基础上，进一步研究了多层网络的同步能力、广义同步、拓扑识别的问题。经过不断努力，得到一些普适的规律和新颖的结论，可以为工程、生物、社会等学科的相应领域提供必要的理论支撑。