权重分布对加权网络效率的影响

加权网络可以对复杂系统的相互作用结构提供更加细致的刻画,而改变边权也成为调整和改善网络性质与功能的新途径.基于已有无权网络的效率概念,文中给出了相似权和相异权网络的网络效率定义,并研究了权重分布对于网络效率的影响.从平权的规则网络出发,通过改变权重的分布形式考察权重分布对网络效率的影响,结果发现,在规则网络上,权重分布随机性的增加提高了网络效率,而在几种常见的权重分布形式中,指数分布对网络效率的改进最为显著.同时,权重随机化之后网络最小生成树的总权重减小,意味着网络的运输成本随着权重异质性的增加而降低.以上结果为深入理解权重对网络结构与功能的影响提供了基础. 关键词： 复杂网络 加权网络 权重 网络效率     

激光时空混沌模型的加权网络投影同步

提出了一种实现加权网络时空混沌投影同步的方法.通过构造合适的Lyapunov函数,确定了加权网络中连接节点之间耦合函数的结构以及网络节点状态方程中分离配置的线性项的系数矩阵的取值范围.以Bragg声光双稳系统作为局域函数,单向耦合映像格子作为空间扩展系统构成激光时空混沌模型.通过仿真模拟检验了采用激光时空混沌模型作为网络节点的加权网络的投影同步效果.结果显示,对于任意的节点之间耦合强度的权重值,加权网络的投影同步均可以实现. 关键词： 投影同步 加权网络 时空混沌 Bragg声光双稳系统     

加权网络中基于冗余边过滤的k-核分解排序算法

k-核分解排序法对于度量复杂网络上重要节点的传播影响力具有重要的理论意义和应用价值,但其排序粗粒化的缺陷也不容忽视.最新研究发现,一些真实网络中存在局域连接稠密的特殊构型是导致上述问题的根本原因之一.当前的解决方法是利用边两端节点的外部连边数度量边的扩散性,采取过滤网络边来减少这种稠密结构给k-核分解过程造成的干扰,但这种方法并没有考虑现实网络上存在权重的普遍性.本文利用节点权重和权重分布重新定义边的扩散性,提出适用于加权网络结构的基于冗余边过滤的k-核分解排序算法:filter-core.通过世界贸易网、线虫脑细胞网和科学家合著网等真实网络的SIR(susceptible-infectedrecovered)传播模型的仿真结果表明,该算法相比其他加权k-核分解法,能够更准确地度量加权网络上具有重要传播影响力的核心节点及核心层.     

复杂网络病毒传播的局域控制研究

从复杂网络的节点路径长度范围的角度来研究病毒传播的局域控制，分析了在不同拓扑结构的复杂网络中进行局域控制的有效性.研究表明，局域控制对WS小世界网络、BA无标度网络和ER随机网络三类复杂网络均有效，但只有WS小世界网络存在零感染的控制范围最优值d=3；对于长程连边的分布存在距离偏好的Kleinberg小世界网络，随着依赖度的增大，病毒传播率临界值增加，同时局域范围控制的效果得到加强. 关键词： 复杂网络 病毒传播 局域控制 路径长度     

一种新型电力网络局域世界演化模型

现实世界中的许多系统都可以用复杂网络来描述,电力系统是人类创造的最为复杂的网络系统之一.当前经典的网络模型与实际电力网络存在较大差异.从电力网络本身的演化机理入手,提出并研究了一种可以模拟电力网络演化规律的新型局域世界网络演化模型.理论分析表明该模型的度分布具有幂尾特性,且幂律指数在3—∞之间可调.最后通过对中国北方电网和美国西部电网的仿真以及和无标度网络、随机网络的对比,验证了该模型可以很好地反映电力网络的演化规律,并且进一步证实了电力网络既不是无标度网络,也不是完全的随机网络. 关键词： 电力网络 演化模型 局域世界 幂律分布     

推广的失活网络动力学同步优化

在不改变网络度分布的条件下,研究了推广的失活网络的同步行为. 应用特征值比R来衡量网络的同步能力,发现同步能力可以通过改变结构参数——激活节点数M来进行优化.特征值比R随M的变化非常敏感,激活节点数M越大,特征值比R越小,同步能力就越强,且在一定范围内遵循R～M^-2.0的幂律关系.通过引入结构微扰,该网络的同步能力也可以得到有效优化. 关键词： 推广的失活网络 同步 特征值比 优化     

环形加权网络的时空混沌延迟同步

研究了环形加权网络的时空混沌延迟同步问题.以随时间和空间演化均呈现混沌行为的时空混沌系统作为网络的节点,通过环形加权连接使所有节点建立关联.基于线性稳定性定理,通过确定网络的最大Lyapunov指数,得到了实现网络延迟同步的条件.在最大Lyapunov指数小于零的区域内,任取节点之间耦合强度的权重值,均可以使整个网络实现延迟同步.采用具有时空混沌行为的自催化反应扩散系统作为网络节点,仿真模拟验证了该方法的有效性. 关键词： 延迟同步 加权网络 时空混沌 Lyapunov指数     

加权复杂网络社团的评价指标及其发现算法分析

节点的聚集现象是复杂网络的重要特性.以往研究主要发现无权复杂网络中的社团,较少涉及加权网络的社团发现.由于加权网络的复杂性远高于无权网络,一般认为加权网络的社团发现是一个较难的问题.本文基于统一的数据基础,从社团评价指标的有效性和现有算法的效果两个角度开展研究.首先,总结了加权网络三种常见的社团评估指标,并在社团大小、密度和局域特点均不同的模拟数据集上分析指标的有效性;其次,针对5个数据集,分析现有的3种加权复杂网络社团发现算法的效果.研究表明:上述指标无论在评价最基本的社团结构,还是在分析结构复杂的社团时都有较大缺欠;现有的加权网络社团发现算法的泛化能力不强.     

一种有效的提高复杂网络同步能力的自适应方法

本文提出了一种根据节点状态来调节网络中边权重的自适应方法(MDMF)来提高网络的同步能力, 总结了网络规模与网络平均速度对同步能力的影响. 研究发现, 通过这种自适应方法, 得到网络的同步能力与网络规模成幂率关系. 在相同网络规模下, 此方法能使网络的同步能力高于无权重网络几个数量级.当网络规模越大时, 提高同步能力越高效.     

一种基于随机行走和策略连接的网络演化模型

本文提出了一个基于随机行走和策略选择的复杂网络局域演化模型RAPA. 新节点加入系统不需要全局知识,而是通过随机行走构造局域世界;然后依据概率采用随机连接,"扶贫"连接或"亲富"连接策略,从局域世界中选择节点增加连接边;最终自组织演化具有幂律特点的复杂网络. 初步的解析计算和仿真实验都表明,RAPA模型不仅重现了具有小世界特性、整体上的无标度特性,还可以演化出小变量饱和以及指数截断等现象,同时也具有明显的聚类特性,并能够构造出同配或异配等不同混合模式的网络. 关键词： 复杂网络 模型 随机行走 策略连接     

Synchronization in Triangled Complex Networks

Using a tunable clustering coefficient model without changing the degree distribution, we investigate the effect of clustering coefficient on synchronization of networks with both unweighted and weighted couplings. For several typical categories of complex networks, the more triangles are in the networks, the worse the synchronizability of the networks is.     

From unweighted to weighted networks with local information

In this paper, we analyze an evolving model with local information which can generate a class of networks by choosing different values of the parameter p. The model introduced exhibits the transition from unweighted networks to weighted networks because the distribution of the edge weight can be widely tuned. With the increase in the local information, the degree correlation of the network transforms from assortative to disassortative. We also study the distribution of the degree, strength and edge weight, which all show crossover between exponential and scale-free. Finally, an application of the proposed model to the study of the synchronization is considered. It is concluded that the synchronizability is enhanced when the heterogeneity of the edge weight is reduced.     

Synchronization in weighted complex networks: Heterogeneity and synchronizability

Synchronization in different types of weighted networks based on a scale-free weighted network model is investigated. It has been argued that heterogeneity suppresses synchronization in unweighted networks [T. Nishikawa, A.E. Motter, Y.C. Lai, F.C. Hoppensteadt, Phys. Rev. Lett. 91 (2003) 014101]. However, it is shown in this work that as the network becomes more heterogeneous, the synchronizability of Type I symmetrically weighted networks, and Type I and Type II asymmetrically weighted networks is enhanced, while the synchronizability of Type II symmetrically weighted networks is weakened.     

Synchronization in a class of weighted complex networks with coupling delays

It is commonly accepted that realistic networks can display not only a complex topological structure, but also a heterogeneous distribution of connection weights. In addition, time delay is inevitable because the information spreading through a complex network is characterized by the finite speeds of signal transmission over a distance. Weighted complex networks with coupling delays have been gaining increasing attention in various fields of science and engineering. Some of the topics of most concern in the field of weighted complex networks are finding how the synchronizability depends on various parameters of the network including the coupling strength, weight distribution and delay. On the basis of the theory of asymptotic stability of linear time-delay systems with complex coefficients, the synchronization stability of weighted complex dynamical networks with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of the synchronization state. Finally, an example is given as an illustration testing the theoretical results.     

Enhancing synchronizability by weight randomization on regular networks

In weighted networks, redistribution of link weights can effectively change the properties of networks, even though the corresponding binary topology remains unchanged. In this paper, the effects of weight randomization on synchronization of coupled chaotic maps is investigated on regular weighted networks. The results reveal that synchronizability is enhanced by redistributing of link weights, i.e. coupled maps reach complete synchronization with lower cost. Furthermore, we show numerically that the heterogeneity of link weights could improve the complete synchronization on regular weighted networks.     

Universality in the synchronization of weighted random networks

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of a few parameters.     

Enhancing synchronizability by rewiring networks

<正>According to different forms of synchronized region,complex networks are divided into typeⅠ(unbounded synchronization region) and typeⅡ(bounded synchronization region) networks.This paper presents a rewiring algorithm to enhance the synchronizability of typeⅠand typeⅡnetworks.By utilizing the algorithm for an unweighted and undirected network,a better synchronizability of network with the same number of nodes and edges can be obtained. Numerical simulations on several different network models are used to support the proposed procedure.The relationship between different topological properties of the networks and the number of rewirings are shown.It finds that the final optimized network is independent of the initial network,and becomes homogeneous.In addition the optimized networks have similar structural properties in the sense of degree,and node and edge betweenness centralities.However,they do not have similar cluster coefficients for typeⅡnetworks.The research may be useful for designing more synchronizable networks and understanding the synchronization behaviour of networks.     

Synchronization speed of identical oscillators on community networks

Synchronizability of complex oscillators networks has attracted much research interest in recent years. In contrast, in this paper we investigate numerically the synchronization speed, rather than the synchronizability or synchronization stability, of identical oscillators on complex networks with communities. A new weighted community network model is employed here, in which the community strength could be tunable by one parameter δ. The results showed that the synchronization speed of identical oscillators on community networks could reach a maximal value when δ is around 0.1. We argue that this is induced by the competition between the community partition and the scale-free property of the networks. Moreover, we have given the corresponding analysis through the second least eigenvalue λ₂ of the Laplacian matrix of the network which supports the previous result that the synchronization speed is determined by the value of λ₂.     

加权方式对网络同步能力的影响

针对真实网络中权值与端点度的相关特性,提出了一种与始点和终点的度 都相关的非对称加权方式.在不同的网络结构下研究加权方式对同步能力的影响. 研究发现网络异质性越强时,通过调节网络权值改变网络同步能力的效果越显著, 而网络越匀质时,调节权值的方式改变网络同步能力的效果越不明显. 仿真实验显示无论在小世界网络还是无标度网络中,网络都是在节点的输入强度为1处获得最优的同步能力.     

Rewiring dynamical networks with prescribed degree distribution for enhancing synchronizability

In this paper, we present an algorithm for enhancing synchronizability of dynamical networks with prescribed degree distribution. The algorithm takes an unweighted and undirected network as input and outputs a network with the same node-degree distribution and enhanced synchronization properties. The rewirings are based on the properties of the Laplacian of the connection graph, i.e., the eigenvectors corresponding to the second smallest and the largest eigenvalues of the Laplacian. A term proportional to the eigenvectors is adopted to choose potential edges for rewiring, provided that the node-degree distribution is preserved. The algorithm can be implemented on networks of any sizes as long as their eigenvalues and eigenvectors can be calculated with standard algorithms. The effectiveness of the proposed algorithm in enhancing the network synchronizability is revealed by numerical simulation on a number of sample networks including scale-free, Watts-Strogatz, and Erdo?s-Re?nyi graphs. Furthermore, a number of network's structural parameters such as node betweenness centrality, edge betweenness centrality, average path length, clustering coefficient, and degree assortativity are tracked as a function of optimization steps.