Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay

Many existing papers investigated the geometric features, control and synchronization of complex dynamical networks provided with certain topology. However, the exact topology of a network is sometimes unknown or uncertain. Based on LaSalle’s invariance principle, we propose an adaptive feedback technique to identify the exact topology of a weighted general complex dynamical network model with time-varying coupling delay. By receiving the network nodes evolution, the topology of such a kind of network with identical or different nodes, or even with varying topology can be monitored. In comparison with previous methods, time delay is taken into account in this simple, analytical and systematic synchronization-based technique. Particularly, the weight configuration matrix is not necessarily symmetric or irreducible, and the inner-coupling matrix need not be symmetric. Illustrative simulations are provided to verify the correctness and effectiveness of the proposed scheme.     

Adaptive projective synchronization in complex networks with time-varying coupling delay

In this Letter, adaptive projective synchronization (PS) between two complex networks with time-varying coupling delay is investigated by the adaptive control method, and this method has been applied to identify the exact topology of a weighted general complex network. To validate the proposed method, the Lü and Qi systems as the nodes of the networks are detailed analysis, and some numerical results show the effectiveness of the present method.     

Fault diagnosis of time-delay complex dynamical networks using output signals

This paper proposes a novel approach for fault diagnosis of a time-delay complex dynamical network.Unlike the other methods,assuming that the dynamics of the network can be described by a linear stochastic model,or using the state variables of nodes in the network to design an adaptive observer,it only uses the output variable of the nodes to design an observer and an adaptive law of topology matrix in the observer of a complex network,leading to simple design of the observer and easy realisation of topology monitoring for the complex networks in real engineering.The proposed scheme can monitor any changes of the topology structure of a time-delay complex network.The effectiveness of this method is successfully demonstrated by virtue of a complex networks with Lorenz model.     

Concentric characterization and classification of complex network nodes: Application to an institutional collaboration network

Differently from theoretical scale-free networks, most real networks present multi-scale behavior, with nodes structured in different types of functional groups and communities. While the majority of approaches for classification of nodes in a complex network has relied on local measurements of the topology/connectivity around each node, valuable information about node functionality can be obtained by concentric (or hierarchical) measurements. This paper extends previous methodologies based on concentric measurements, by studying the possibility of using agglomerative clustering methods, in order to obtain a set of functional groups of nodes, considering particular institutional collaboration network nodes, including various known communities (departments of the University of São Paulo). Among the interesting obtained findings, we emphasize the scale-free nature of the network obtained, as well as identification of different patterns of authorship emerging from different areas (e.g. human and exact sciences). Another interesting result concerns the relatively uniform distribution of hubs along concentric levels, contrariwise to the non-uniform pattern found in theoretical scale-free networks such as the BA model.     

Studies on controllability of directed networks with extremal optimization

Almost all natural, social and man-made-engineered systems can be represented by a complex network to describe their dynamic behaviors. To make a real-world complex network controllable with its desired topology, the study on network controllability has been one of the most critical and attractive subjects for both network and control communities. In this paper, based on a given directed–weighted network with both state and control nodes, a novel optimization tool with extremal dynamics to generate an optimal network topology with minimum control nodes and complete controllability under Kalman’s rank condition has been developed. The experimental results on a number of popular benchmark networks show the proposed tool is effective to identify the minimum control nodes which are sufficient to guide the whole network’s dynamics and provide the evolution of network topology during the optimization process. We also find the conclusion: “the sparse networks need more control nodes than the dense, and the homogeneous networks need fewer control nodes compared to the heterogeneous” (Liu et al., 2011  [18]), is also applicable to network complete controllability. These findings help us to understand the network dynamics and make a real-world network under the desired control. Moreover, compared with the relevant research results on structural controllability with minimum driver nodes, the proposed solution methodology may also be applied to other constrained network optimization problems beyond complete controllability with minimum control nodes.     

基于传播免疫的复杂网络可控性研究

复杂网络控制反映了人类对复杂系统的认识深度和改造能力. 最新研究成果基于线性系统控制理论建立了复杂网络可控性的理论架构, 能够发现任意拓扑结构的线性时不变复杂网络中控制全部节点状态的最小驱动节点集, 但是该模型未考虑免疫节点或失效节点对控制信号传播的阻断.在继承该模型优点的前提下, 重新构建了基于传播免疫的复杂网络控制模型.在采用分属于随机免疫和目标免疫两种策略的 4个方法确定免疫节点的情况下,分析14个真实网络的可控性.结果表明:如果将网络中度数、 介数和紧密度指标较高的节点作为免疫节点,将极大地提高控制复杂网络的难度. 从而在一定程度上丰富了以往模型的结论.     

Geographical Effects on Complex Networks

We investigate how the geographical structure of a complex network affects its network topology, synchronization and the average spatial length of edges. The geographical structure means that the connecting probability of two nodes is related to the spatial distance of the two nodes. Our simulation results show that the geographical structure changes the network topology. The synchronization tendency is enhanced and the average spatial length of edges is enlarged when the node can randomly connect to the further one. Analytic results support our understanding of the phenomena.     

Geographical Effects on Complex Networks

We investigate how the geographical structure of a complex network affects its network topology, synchronization and the average spatial length of edges. The geographical structure means that the connecting probability of two nodes is related to the spatial distance of the two nodes. Our simulation results show that the geographical structure changes the network topology. The synchronization tendency is enhanced and the average spatial length of edges is enlarged when the node can randomly connect to the further one. Analytic results support our understanding of the phenomena.     

Evolution of the Internet AS-level topology:From nodes and edges to components

Studying the topology of infrastructure communication networks(e.g., the Internet) has become a means to understand and develop complex systems. Therefore, investigating the evolution of Internet network topology might elucidate disciplines governing the dynamic process of complex systems. It may also contribute to a more intelligent communication network framework based on its autonomous behavior. In this paper, the Internet Autonomous Systems(ASes) topology from 1998 to 2013 was studied by deconstructing and analysing topological entities on three different scales(i.e., nodes,edges and 3 network components: single-edge component M1, binary component M2 and triangle component M3). The results indicate that: a) 95% of the Internet edges are internal edges(as opposed to external and boundary edges); b) the Internet network consists mainly of internal components, particularly M2 internal components; c) in most cases, a node initially connects with multiple nodes to form an M2 component to take part in the network; d) the Internet network evolves to lower entropy. Furthermore, we find that, as a complex system, the evolution of the Internet exhibits a behavioral series,which is similar to the biological phenomena concerned with the study on metabolism and replication. To the best of our knowledge, this is the first study of the evolution of the Internet network through analysis of dynamic features of its nodes,edges and components, and therefore our study represents an innovative approach to the subject.     

Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics

This paper considers the global stability of controlling an uncertain complex network to a homogeneous trajectory of the uncoupled system by a local pinning control strategy. Several sufficient conditions are derived to guarantee the network synchronisation by investigating the relationship among pinning synchronisation, network topology, and coupling strength. Also, some fundamental and yet challenging problems in the pinning control of complex networks are discussed: (1) what nodes should be selected as pinned candidates? (2) How many nodes are needed to be pinned for a fixed coupling strength? Furthermore, an adaptive pinning control scheme is developed. In order to achieve synchronisation of an uncertain complex network, the adaptive tuning strategy of either the coupling strength or the control gain is utilised. As an illustrative example, a network with the Lorenz system as node self-dynamics is simulated to verify the efficacy of theoretical results.     

带有层级结构的复杂网络级联失效模型

针对现实世界的网络中普遍存在的层级结构建立一个级联失效模型, 该模型可用于优化金融、物流网络设计. 选择的层级网络模型具有树形骨架和异质的隐含连接, 并且骨架中每层节点拥有的分枝数服从正态分布. 级联失效模型中对底层节点的打击在不完全信息条件下进行, 也即假设打击者无法观察到隐含连接. 失效节点的负载重分配考虑了层级异质性, 它可以选择倾向于向同级或高层级完好节点分配额外负载. 仿真实验表明, 层级网络的拓扑结构随连接参数变化逐渐从小世界网络过渡到随机网络. 网络级联失效规模随隐含连接比例呈现出先增加后降低的规律. 负载重分配越倾向于高层级节点, 网络的抗毁损性越高. 同时, 由于连接参数会改变隐含连接在不同层级之间的分布, 进而对网络的抗毁损性产生显著影响, 为了提高网络抗毁损能力, 设计网络、制定管理控制策略时应合理设定连接参数. 关键词： 复杂网络 级联失效 层级结构     

A Generalized Voter Model on Complex Networks

We study a generalization of the voter model on complex networks, focusing on the scaling of mean exit time. Previous work has defined the voter model in terms of an initially chosen node and a randomly chosen neighbor, which makes it difficult to disentangle the effects of the stochastic process itself relative to the network structure. We introduce a process with two steps, one that selects a pair of interacting nodes and one that determines the direction of interaction as a function of the degrees of the two nodes and a parameter α which sets the likelihood of the higher degree node giving its state to the other node. Traditional voter model behaviors can be recovered within the model, as well as the invasion process. We find that on a complete bipartite network, the voter model is the fastest process. On a random network with power law degree distribution, we observe two regimes. For modest values of α, exit time is dominated by diffusive drift of the system state, but as the high-degree nodes become more influential, the exit time becomes dominated by frustration effects dependent on the exact topology of the network.     

A novel method to identify influential nodes based on hybrid topology structure

With the increasing popularity of rail transit and the increasing number of light rail trips, the vulnerability of rail transit has become increasingly prominent. Once the rail transit is maliciously broken or the light rail station is repaired, it may lead to large-scale congestion or even the paralysis of the whole rail transit network. Hence, it is particularly important to identify the influential nodes in the rail transit network. Existing identifying methods considered a single scenario on either betweenness centrality (BC) or closeness centrality. In this paper, we propose a hybrid topology structure (HTS) method to identify the critical nodes based on complex network theory. Our proposed method comprehensively considers the topology of the node itself, the topology of neighbor nodes, and the global influence of the node itself. Finally, the susceptible–infected–recovered (SIR) model, the monotonicity (M), the distinct metric (DM), the Jaccard similarity coefficient (JSC), and the Kendall correlation coefficient (KC) are utilized to evaluate the proposed method over the six real-world networks. Experimental results confirm that the proposed method achieves higher performance than existing methods in identifying networks.     

基于动力中继的小世界复杂电机网络混沌同步控制

利用链式结构中间节点参数不匹配能降低两个非直接相连外部节点的同步耦合强度临界值,促进两节点同步的特性,对一个双向耦合的小世界电机网络进行同步控制.首先从外部增加参数不匹配的中继节点,通过动力中继降低整个网络的同步耦合强度阈值,从而促进整个电机网络的同步,然后分析动力中继如何作用于网络,最后用数值仿真验证该方法的有效性.     

Communication boundaries in networks

We investigate and quantify the interplay between topology and the ability to send specific signals in complex networks. We find that in a majority of investigated real-world networks the ability to communicate is favored by the network topology at small distances, but disfavored at larger distances. We further suggest how the ability to locate specific nodes can be improved if information associated with the overall traffic in the network is available.     

Network evolution based on minority game with herding behavior

The minority game (MG) is used as a source of information to design complex networks where the nodes represent the playing agents. Differently from classical MG consisting of independent agents, the current model rules that connections between nodes are dynamically inserted or removed from the network according to the most recent game outputs. This way, preferential attachment based on the concept of social distance is controlled by the agents wealth. The time evolution of the network topology, quantitatively measured by usual parameters, is characterized by a transient phase followed by a steady state, where the network properties remain constant. Changes in the local landscapes around individual nodes depend on the parameters used to control network links. If agents are allowed to access the strategies of their network neighbors, a feedback effect on the network structure and game outputs is observed. Such effect, known as herding behavior, considerably changes the dependence of volatility σ on memory size: it is shown that the absolute value of σ as well as the corresponding value of memory size depend both on the network topology and on the way along which the agents make their playing decisions in each game round.     

Self-Organized Optimization of Transport on Complex Networks

We propose a self-organized optimization mechanism to improve the transport capacity of complex gradient networks.We find that,regardless of network topology,the congestion pressure can be strongly reduced by the self-organized optimization mechanism.Furthermore,the random scale-free topology is more efficient to reduce congestion compared with the random Poisson topology under the optimization mechanism.The reason is that the optimization mechanism introduces the correlations between the gradient field and the local topology of the substrate network.Due to the correlations,the cutoff degree of the gradient network is strongly reduced and the number of the nodes exerting their maximal transport capacity consumedly increases.Our work presents evidence supporting the idea that scale-free networks can efficiently improve their transport capacity by selforganized mechanism under gradient-driven transport mode.     

A Robustness Model of Complex Networks with Tunable Attack Information Parameter

We introduce a novel model for robustness of complex with a tunable attack information parameter. The random failure and intentional attack known are the two extreme cases of our model. Based on the model, we study the robustness of complex networks under random information and preferential information, respectively. Using the generating function method, we derive the exact value of the critical removal fraction of nodes for the disintegration of networks and the size of the giant component. We show that hiding just a small fraction of nodes randomly can prevent a scale-free network from collapsing and detecting just a small fraction of nodes preferentially can destroy a scale-free network.     

Change of network load due to node removal

The interplay between topology changes and the redistribution of traffic plays a significant role in many real-world networks. In this paper we study how the load of the remaining network changes when nodes are removed. This removal operation can model attacks and errors in networks, or the planned control of network topology. We consider a scenario similar to the data communication networks, and measure the load of a node by its betweenness centrality. By analysis and simulations, we show that when a single node is removed, the change of the remaining network’s load is positively correlated with the degree of the removed node. In multiple-node removal, by comparing several node removal schemes, we show in detail how significantly different the change of the remaining network’s load will be between starting the removal from small degree/betweenness nodes and from large degree/betweenness nodes. Moreover, when starting the removal from small degree/betweenness nodes, we not only observe that the remaining network’s load decreases, which is consistent with previous studies, but also find that the load of hubs keeps decreasing. These results help us to make a deeper understanding about the dynamics after topology changes, and are useful in planned control of network topology.     

A generalized approach to complex networks

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the network topology to new network growth models. First, the concepts of node degree and clustering coefficient are extended in order to characterize not only specific nodes, but any generic subnetwork. Second, the consideration of distance transform and rings are used to further extend those concepts in order to obtain a signature, instead of a single scalar measurement, ranging from the single node to whole graph scales. The enhanced discriminative potential of such extended measurements is illustrated with respect to the identification of correspondence between nodes in two complex networks, namely a protein-protein interaction network and a perturbed version of it.