Optimization-based topology identification of complex networks

In many cases, the topological structures of a complex network are unknown or uncertain, and it is of significance to identify the exact topological structure. An optimization-based method of identifying the topological structure of a complex network is proposed in this paper. Identification of the exact network topological structure is converted into a minimal optimization problem by using the estimated network. Then, an improved quantum-behaved particle swarm optimization algorithm is used to solve the optimization problem. Compared with the previous adaptive synchronization-based method, the proposed method is simple and effective and is particularly valid to identify the topological structure of synchronization complex networks. In some cases where the states of a complex network are only partially observable, the exact topological structure of a network can also be identified by using the proposed method. Finally, numerical simulations are provided to show the effectiveness of the proposed method.     

Topology identification of weighted complex dynamical networks

Recently, various papers investigated the geometry features, synchronization and control of complex network provided with certain topology. While, the exact topology of a network is sometimes unknown or uncertain. Using Lyapunov theory, we propose an adaptive feedback controlling method to identify the exact topology of a rather general weighted complex dynamical network model. By receiving the network nodes evolution, the topology of such kind of network with identical or different nodes, or even with switching topology can be monitored. Experiments show that the methods presented in this paper are of high accuracy with good performance.     

Effect of incubation period on epidemic spreading in complex networks

We study the effect of incubation period on epidemic spreading in the Barabasi--Albert scale-free network and the Watts--Strogatz small world network by using a Suspectable-Incubated-Infected-Suspectable model. Our analytical investigations show that the epidemic threshold is independent of incubation period in both networks, which is verified by our large-scale simulation results. We also investigate the effect of incubation period on the epidemic dynamics in a supercritical regime. It is found that with the increase of incubation period Ω , a damped oscillation evolution of ρ_T(the ratio of persons in incubated state) appears and the time needed to reach a saturation value increases. Moreover, the steady value of ρ_T increases and approaches to an asymptotic constant with the value of {\it\Omega} increasing. As a result, the infected ratio ρ_I decreases with the increase of Ω according to a power law.     

Synchronization of spatiotemporal chaos in a class of complex dynamical networks

This paper studies the synchronization of complex dynamical networks constructed by spatiotemporal chaotic systems with unknown parameters. The state variables in the systems with uncertain parameters are used to construct the parameter recognizers, and the unknown parameters are identified. Uncertain spatiotemporal chaotic systems are taken as the nodes of complex dynamical networks, connection among the nodes of all the spatiotemporal chaotic systems is of nonlinear coupling. The structure of the coupling functions between the connected nodes and the control gain are obtained based on Lyapunov stability theory. It is seen that stable chaos synchronization exists in the whole network when the control gain is in a certain range. The Gray--Scott models which have spatiotemporal chaotic behaviour are taken as examples for simulation and the results show that the method is very effective.     

Traffic of indistinguishable particles in complex networks

In this paper, we apply a simple walk mechanism to the study of the traffic of many indistinguishable particles in complex networks. The network with particles stands for a particle system, and every vertex in the network stands for a quantum state with the corresponding energy determined by the vertex degree. Although the particles are indistinguishable, the quantum states can be distinguished. When the many indistinguishable particles walk randomly in the system for a long enough time and the system reaches dynamic equilibrium, we find that under different restrictive conditions the particle distributions satisfy different forms, including the Bose--Einstein distribution, the Fermi--Dirac distribution and the non-Fermi distribution (as we temporarily call it). As for the Bose--Einstein distribution, we find that only if the particle density is larger than zero, with increasing particle density, do more and more particles condense in the lowest energy level. While the particle density is very low, the particle distribution transforms from the quantum statistical form to the classically statistical form, i.e., transforms from the Bose distribution or the Fermi distribution to the Boltzmann distribution. The numerical results fit well with the analytical predictions.     

复Ginzburg-Landau方程时空混沌的网络同步与参量辨识

研究了参量未知的时空混沌系统构成复杂网络的同步与参量辨识问题. 设计的参量辨识律可以有效地辨识复杂网络中所有节点时空混沌系统中的未知参量. 基于稳定性定理, 通过构造适当的Lyapunov函数, 确定了网络完全同步的条件. 以参量未知的一维复Ginzburg-Landau方程作为网络节点为例, 通过仿真模拟检验了参量辨识律以及同步方法的有效性.     

Topology identification for a class of complex dynamical networks using output variables

A problem of topology identification for complex dynamical networks is investigated in this paper. An adaptive observer is proposed to identify the topology of a complex dynamical networks based on the Lyapunov stability theory. Here the output of the network and the states of the observer are used to construct the updating law of the topology such that the communication resources from the network to its observer are saved. Some convergent criteria of the adaptive observer are derived in the form of linear inequality matrices. Several numerical examples are shown to demonstrate the effectiveness of the proposed observer.     

基于时间序列符号化模式表征的有向加权复杂网络

时间序列复杂网络分析近些年已发展成为非线性信号分析领域的一个国际热点课题.为了能更有效地挖掘时间序列(特别是非线性时间序列)中的结构特征,同时简化时间序列分析的复杂度,提出了一种新的基于时间序列符号化结合滑窗技术模式表征的有向加权复杂网络建网方法.该方法首先按照等概率区段划分的方式将时间序列做符号化处理,结合滑窗技术确定不同时刻的符号化模式作为网络的节点;然后将待分析时间序列符号化模式的转换频次和方向作为网络连边的权重和方向,从而建立时间序列有向加权复杂网络.通过对Logistic系统不同参数设置对应的时间序列复杂网络建网测试结果表明,相比经典的可视图建网方法,本文方法的网络拓扑能更简洁、直观地展示时间序列的结构特征.进而,将本文方法应用于规则排列采集的自然风场信号分析,其网络特性指标能较准确地预测采集信号的排布规律,而可视图建网方法的网络特性指标没有任何规律性的结果.     

Traffic dynamics on layered complex networks

To minimize traffic congestion, understanding how traffic dynamics depend on network structure is necessary. Many real-world complex systems can be described as multilayer structures. In this paper, we introduce the idea of layers to establish a traffic model of two-layer complex networks. By comparing different two-layer complex networks based on random and scale-free networks, we find that the physical layer is much more important to the network capacity of two-layer complex networks than the logical layer. Two-layer complex networks with a homogeneous physical topology are found to be more tolerant to congestion. Moreover, simulation results show that the heterogeneity of logical and physical topologies makes the packet-delivery process of two-layer networks more efficient in the free-flow state, without the occurrence of traffic congestion.     

Mirror nodes in growing random networks

In this article, we consider mirror nodes, which are widely used to reduce local burden, and present two models that are practical for the Internet and probably some other networks. One model introduces an upper limit to the number of links that a node can have, beyond which the node will share the total links with a newly introduced one. Similarly, in the second model, if the number of links exceeds a limit, a new node will be introduced. Unlike the first model, the new node shares with the old one the chance of receiving new links but not the existing links. These models are analytically treated, and from the degree distribution, we can see that the number of nodes with medium links (half the upper limit) increases at the expense of the loss of highly connected nodes. By reducing the burden, this may improve the robustness of the networks.     

基于有限穿越可视图的时间序列网络模型

提出了一种改进的时间序列有限穿越可视图建网方法,并对三种可视图(可视图、水平可视图、有限穿越可视图)网络度分布进行了评价.结果表明:水平可视图网络均无法有效识别各类时间序列信号(周期、分形、混沌);对分形信号,可视图及有限穿越可视图网络均具有无标度幂律形式,但抗噪能力较差;对周期信号及混沌信号,有限穿越可视图网络比可视图具有更强的抗噪性.在此基础上,采用有限穿越可视图网络从油气水三相流电导波动信号中提取了度分布特征参数,通过其特征参数组合实现了对三种典型三相流流型(水包油泡状流、水包油泡状-段塞过渡流型及水包油段塞流)较好的辨识效果.     

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.     

复杂网络上灾害蔓延动力学研究

针对关键生命线系统，如电网、供水网、供气网、交通网、通信网等的一些共性特征，建立一个普适性的灾害蔓延动力学模型. 这个模型考虑网络结点的自修复功能、灾害蔓延机制和内部随机噪声，并研究自修复因子、延迟时间因子和噪声强度三个重要特征参数对三种网络(随机网络、无标度网络和小世界网络)结点修复率和崩溃结点数的影响. 模拟结果与这些实际生命线系统的特征一致，表明所建立的模型可以有效地模拟生命线系统的灾害演化动力学. 关键词： 复杂网络 生命线系统 灾害蔓延     

An extended improved global structure model for influential node identification in complex networks

Accurate identification of influential nodes facilitates the control of rumor propagation and interrupts the spread of computer viruses. Many classical approaches have been proposed by researchers regarding different aspects. To explore the impact of location information in depth, this paper proposes an improved global structure model to characterize the influence of nodes. The method considers both the node's self-information and the role of the location information of neighboring nodes. First, degree centrality of each node is calculated, and then degree value of each node is used to represent self-influence, and degree values of the neighbor layer nodes are divided by the power of the path length, which is path attenuation used to represent global influence. Finally, an extended improved global structure model that considers the nearest neighbor information after combining self-influence and global influence is proposed to identify influential nodes. In this paper, the propagation process of a real network is obtained by simulation with the SIR model, and the effectiveness of the proposed method is verified from two aspects of discrimination and accuracy. The experimental results show that the proposed method is more accurate in identifying influential nodes than other comparative methods with multiple networks.     

Efficient algorithm based on neighborhood overlap for community identification in complex networks

Community structure is an important feature in many real-world networks. Many methods and algorithms for identifying communities have been proposed and have attracted great attention in recent years. In this paper, we present a new approach for discovering the community structure in networks. The novelty is that the algorithm uses the strength of the ties for sorting out nodes into communities. More specifically, we use the principle of weak ties hypothesis to determine to what community the node belongs. The advantages of this method are its simplicity, accuracy, and low computational cost. We demonstrate the effectiveness and efficiency of our algorithm both on real-world networks and on benchmark graphs. We also show that the distribution of link strength can give a general view of the basic structure information of graphs.     

节点中心性对复杂网络传播模式的影响分析

在众多的重要节点评估方法研究中,具有较高中心性的节点一直是关注的焦点,许多传播行为的研究也主要围绕高中心性节点展开,因此在一定程度上忽略了低中心性节点对传播行为的影响.本文从传播异构性角度,通过初始感染最大中心性节点和最小中心性节点揭示网络结构异构性对信息传播的影响.实验结果表明,传播过程中存在"链型"和"扇型"两种传播模式,在初始感染比例不断提升的情况下,两种传播模式的相互转换引发传播速率的变化,进一步促使非线性传播规模交叉现象的产生.这一现象说明,在宏观的信息传播过程中,最小中心性节点的影响力不容忽视,尤其在初始感染比例升高时,最小中心性节点比最大中心性节点更具传播优势.     

Synchronization of impulsively coupled complex networks

We investigate the synchronization of complex networks,which are impulsively coupled only at discrete instants.Based on the comparison theory of impulsive differential systems,a distributed impulsive control scheme is proposed for complex dynamical networks to achieve synchronization.The proposed scheme not only takes into account the influence of all nodes to network synchronization,which depends on the weight of each node in the network,but also provides us with a flexible method to select the synchronized state of the network.In addition,it is unnecessary for the impulsive coupling matrix to be symmetrical.Finally,the proposed control scheme is applied to a chaotic Lorenz network and Chua’s circuit network.Numerical simulations are used to illustrate the validity of this control scheme.     

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.     

叶子节点对于网络同步能力影响的研究

系统考察了叶子节点对于网络同步能力的影响,发现随着叶子节点比例的增加,网络的同步能力下降,同时给出了数值结果以及理论解释. 关键词： 复杂网络 叶子节点 同步能力