复杂动力网络的拓扑识别：从单层到多层
发布时间：2018-09-08 15:21
【摘要】：网络的拓扑结构表示其各个节点之间的相互连接关系,在决定网络的演化机制和功能行为上起着重要作用,是分析预测和控制真实的复杂网络动力学行为的前提条件.然而对于真实的复杂网络而言,精确的拓扑结构往往是未知或者部分未知的,因此如何从已检测到的节点动力学变量反演出网络的拓扑结构就显得尤为重要,这就是具有广泛实际背景的复杂动力网络的拓扑识别问题,也是复杂网络科学发展研究中的一个具有挑战性的问题.近几年,复杂网络拓扑识别逐渐引起了国内外许多学者的关注,对此展开了大量的研究工作,并在相对理想化的单层网络拓扑结构识别问题上取得了较好的研究结果.本文主要对含有随机扰动和耦合时滞的复杂网络拓扑识别问题进行研究,并试图将研究结果从单层网络拓展到多层网络.相比单层网络而言,多层网络更能模拟真实的网络系统,描述真正的网络情景,因此随着复杂网络科学的发展,单层网络已经不能满足研究实际复杂系统的要求,而对多层网络的研究和刻画显得迫切需要,这可以为探索大规模网络的动力学演化机制及重塑网络结构等问题奠定基础,为信息、生物、社会等众多学科的发展和研究提供新的视角和方法.文章一共分为6章,第1章简要介绍本文的研究背景和研究现状,第2章给出与后续内容相关的基础知识,第3到5章重点介绍本文所研究的相关工作,在此基础上,第6章给出总结与对未来工作的展望.文章的主要内容和创新之处有如下几点：第3章首先研究基于完全同步的噪声扰动下的单层时滞复杂动力网络的结构识别,将拓扑结构未知的原网络看做驱动网络,通过构造不含噪声的响应网络和设计合适的控制器,并结合随机微分方程稳定性理论来自适应地识别驱动网络的拓扑结构.值得指出的是,所考虑的网络模型含有随机噪声的扰动,但是为识别其结构而构造的网络仅将驱动网络的节点状态作为控制输入而不含噪声,这在一定程度上大大简化了识别程序,从而提高识别效率.此外,所提出的控制方法可以有效的用于网络隐藏源或者隐藏信息的探测,这也是一个新的发现,可以为工程实践中网络拓扑参数的追踪和隐藏源的定位提供一定的理论指导和方法基础.第4章在上一章基础上给出基于广义同步的网络拓扑识别.本章通过自适应的控制技术使得未知结构网络与构造的响应网络达到广义同步,并且原网络未知的拓扑参数得以识别,而响应网络的结构可以是已知的,未知的,甚至可以是不连通的孤立节点.值得指出的该方法不仅可以用于探测复杂系统的部分结构信息,以及对隐藏源的定位,而且在拓扑结构未知的网络的节点动力学比较复杂或者维数较高时,辅助的响应网络的结构却可以非常简单(表现在维数较低,节点动力学简单等),这是一个前所未有的优势.第5章讨论基于辅助系统法的双层网络识别.对于多层网络我们往往只能获得有限的节点信息或部分层的信息,因此这里所考虑的网络是一个层间单向一一对应的双层网络,将输出层看做驱动层,输入层看做响应层,通过构造与响应层有相同结构的辅助层和设计简单的自适应控制器来识别响应层的拓扑结构.该方法最大的特点就是控制器比较简单,可以大大缩减控制输入信息量,提高控制识别效率.仿真实验验证了理论结果的有效性,同时也得出了关于层间耦合强度变化时识别时间如何变化这一有意思的结论.希望能为谣言传播,伪信息传播的路线和源头定位提供一定的理论基础.
[Abstract]:The topological structure of a network represents the interconnection between its nodes and plays an important role in determining the evolution mechanism and functional behavior of the network. It is a prerequisite for analyzing, predicting and controlling the dynamic behavior of a real complex network. In recent years, topology identification of complex dynamical networks is a challenging problem in the scientific development of complex networks. Many scholars at home and abroad pay more and more attention to this problem, and a lot of research work has been carried out, and good results have been obtained on the problem of identifying the topological structure of relatively ideal single-layer networks. Single-layer network extends to multi-layer network. Compared with single-layer network, multi-layer network can better simulate the real network system and describe the real network scenario. Therefore, with the development of complex network science, single-layer network can no longer meet the requirements of researching the actual complex system, and it is urgent to study and characterize multi-layer network. In order to lay a foundation for exploring the dynamic evolution mechanism of large-scale networks and reshaping the network structure, and to provide a new perspective and method for the development and research of information, biology, society and many other disciplines, this paper is divided into six chapters. Chapter 1 briefly introduces the research background and current situation of this paper. Chapter 2 gives the basis related to the follow-up content. Chapters 3 to 5 focus on the related work of this paper, and on this basis, Chapter 6 gives a summary and outlook for future work. The main contents and innovations of this paper are as follows: Chapter 3 first studies the structure identification of single-layer complex dynamic networks with time-delay based on completely synchronous noise disturbances, and the topological junction is proposed. The original network with unknown structure is regarded as a driving network. The topology of the driving network can be adaptively identified by constructing a response network without noise and designing an appropriate controller. It is worth pointing out that the network model considered contains disturbances of random noise but is structured to identify its structure. In addition, the proposed control method can be effectively used to detect hidden sources or hidden information in the network, which is also a new discovery and can be used in engineering practice. Chapter 4 gives the topology identification based on generalized synchronization. In this chapter, adaptive control technology is used to make the unknown network and the constructed response network achieve generalized synchronization, and the original network is unknown. The structure of the response network can be known, unknown, or even disconnected isolated nodes. It is worth pointing out that this method can be used not only to detect some structural information of complex systems, but also to locate hidden sources. Moreover, the node dynamics of the network with unknown topological structure is complex or even unconnected. Chapter 5 discusses two-layer network identification based on auxiliary system method. For multi-layer networks, we can only obtain limited node information or part of the layer information, therefore, we can only obtain limited node information. The network considered here is a two-layer network with one-to-one correspondence between layers. The output layer is regarded as the driving layer, the input layer as the response layer, and the topology of the response layer is identified by constructing an auxiliary layer with the same structure as the response layer and designing a simple adaptive controller. The simulation results show the effectiveness of the theoretical results and the interesting conclusion about how to change the identification time when the coupling strength between layers changes. It is hoped that this paper can provide a theoretical basis for rumor propagation, the route of false information propagation and the source location. Foundation.
【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O157.5
[Abstract]:The topological structure of a network represents the interconnection between its nodes and plays an important role in determining the evolution mechanism and functional behavior of the network. It is a prerequisite for analyzing, predicting and controlling the dynamic behavior of a real complex network. In recent years, topology identification of complex dynamical networks is a challenging problem in the scientific development of complex networks. Many scholars at home and abroad pay more and more attention to this problem, and a lot of research work has been carried out, and good results have been obtained on the problem of identifying the topological structure of relatively ideal single-layer networks. Single-layer network extends to multi-layer network. Compared with single-layer network, multi-layer network can better simulate the real network system and describe the real network scenario. Therefore, with the development of complex network science, single-layer network can no longer meet the requirements of researching the actual complex system, and it is urgent to study and characterize multi-layer network. In order to lay a foundation for exploring the dynamic evolution mechanism of large-scale networks and reshaping the network structure, and to provide a new perspective and method for the development and research of information, biology, society and many other disciplines, this paper is divided into six chapters. Chapter 1 briefly introduces the research background and current situation of this paper. Chapter 2 gives the basis related to the follow-up content. Chapters 3 to 5 focus on the related work of this paper, and on this basis, Chapter 6 gives a summary and outlook for future work. The main contents and innovations of this paper are as follows: Chapter 3 first studies the structure identification of single-layer complex dynamic networks with time-delay based on completely synchronous noise disturbances, and the topological junction is proposed. The original network with unknown structure is regarded as a driving network. The topology of the driving network can be adaptively identified by constructing a response network without noise and designing an appropriate controller. It is worth pointing out that the network model considered contains disturbances of random noise but is structured to identify its structure. In addition, the proposed control method can be effectively used to detect hidden sources or hidden information in the network, which is also a new discovery and can be used in engineering practice. Chapter 4 gives the topology identification based on generalized synchronization. In this chapter, adaptive control technology is used to make the unknown network and the constructed response network achieve generalized synchronization, and the original network is unknown. The structure of the response network can be known, unknown, or even disconnected isolated nodes. It is worth pointing out that this method can be used not only to detect some structural information of complex systems, but also to locate hidden sources. Moreover, the node dynamics of the network with unknown topological structure is complex or even unconnected. Chapter 5 discusses two-layer network identification based on auxiliary system method. For multi-layer networks, we can only obtain limited node information or part of the layer information, therefore, we can only obtain limited node information. The network considered here is a two-layer network with one-to-one correspondence between layers. The output layer is regarded as the driving layer, the input layer as the response layer, and the topology of the response layer is identified by constructing an auxiliary layer with the same structure as the response layer and designing a simple adaptive controller. The simulation results show the effectiveness of the theoretical results and the interesting conclusion about how to change the identification time when the coupling strength between layers changes. It is hoped that this paper can provide a theoretical basis for rumor propagation, the route of false information propagation and the source location. Foundation.
【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O157.5
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