Analysis of the Chinese air route network as a complex network

The air route network, which supports all the flight activities of the civil aviation, is the most fundamental infrastructure of air traffic management system. In this paper, we study the Chinese air route network (CARN) within the framework of complex networks. We find that CARN is a geographical network possessing exponential degree distribution, low clustering coefficient, large shortest path length and exponential spatial distance distribution that is obviously different from that of the Chinese airport network (CAN). Besides, via investigating the flight data from 2002 to 2010, we demonstrate that the topology structure of CARN is homogeneous, howbeit the distribution of flight flow on CARN is rather heterogeneous. In addition, the traffic on CARN keeps growing in an exponential form and the increasing speed of west China is remarkably larger than that of east China. Our work will be helpful to better understand Chinese air traffic systems.     

基于复杂网络理论的多元混合空管技术保障系统网络特征分析

为提高空管技术保障系统应对突发事件的能力,本文以空管技术保障系统导航、通信、监视设备覆盖的航路结构为基础,构建系统对应的空间网络模型.提出从灵活性、鲁棒性、高效性三个方面度量空管技术保障系统网络特性,对北京、上海、广州、昆明、沈阳、兰州飞行情报区的空管技术保障系统网络的平均度、度分布、度-度相关性、聚集系数、平均路径长度、直径等进行分析.分析结果显示,各飞行情报区空管技术保障系统的平均聚集系数在0.25—0.39之间,网络聚集程度偏低;网络平均路径长度为3.4,表现出小世界网络特征;度值3时服从幂律分布,度-度分布不表现出正相关或负相关.对网络进行基于度优先的和随机的抗毁性测度,空管技术保障系统网络抗毁性较差,网络的可靠性由少数核心节点决定,应对核心节点进行目标免疫,提高网络的抗毁性.这些规律为空管技术保障系统能力提升、新建扩建提供理论依据,对降低突发事件对空管系统保障能力的影响,保障空中交通持续安全具有现实意义.     

Analysis of the Structure and Dynamics of European Flight Networks

We analyze structure and dynamics of flight networks of 50 airlines active in the European airspace in 2017. Our analysis shows that the concentration of the degree of nodes of different flight networks of airlines is markedly heterogeneous among airlines reflecting heterogeneity of the airline business models. We obtain an unsupervised classification of airlines by performing a hierarchical clustering that uses a correlation coefficient computed between the average occurrence profiles of 4-motifs of airline networks as similarity measure. The hierarchical tree is highly informative with respect to properties of the different airlines (for example, the number of main hubs, airline participation to intercontinental flights, regional coverage, nature of commercial, cargo, leisure or rental airline). The 4-motif patterns are therefore distinctive of each airline and reflect information about the main determinants of different airlines. This information is different from what can be found looking at the overlap of directed links.     

Analyzing the causation of a railway accident based on a complex network

In this paper, a new model is constructed for the causation analysis of railway accident based on the complex network theory. In the model, the nodes are defined as various manifest or latent accident causal factors. By employing the complex network theory, especially its statistical indicators, the railway accident as well as its key causations can be analyzed from the overall perspective. As a case, the ＂7.23＂ China-Yongwen railway accident is illustrated based on this model. The results show that the inspection of signals and the checking of line conditions before trains run played an important role in this railway accident. In conclusion, the constructed model gives a theoretical clue for railway accident prediction and, hence, greatly reduces the occurrence of railway accidents.     

利用复杂网络研究中国温度序列的拓扑性质

依据粗粒化方法,将中国1961—2002年逐日平均温度序列转化为由5个特征字符{R,r,e,d,D}构成的温度符号序列.以符号序列中的125种3字串组成的温度波动模态为网络的节点(即连续4d的温度波动组合),并按照时间顺序连边,构建有向加权的温度波动网络,进而将温度波动模态间的相互作用等综合信息蕴含于网络的拓扑结构之中.对随机序列和Lorenz系统的混沌序列分别构建随机和混沌波动网络.计算三种网络的度与度分布、聚类系数、最短路径长度等动 关键词： 气候变化 气候复杂网络 拓扑结构     

中国城市航空网络的实证研究与分析

以城市为节点，城市间直航线路为边，实证地研究了中国城市航空网络的拓扑性质.研究表明，中国城市航空网络是一个小世界网络，具有短的平均路径长度和大的簇系数，且其度分布服从双段幂律分布.它的度度相关性质与世界航空网络和北美航空网络都不相同.当度较小时，世界航空网络和北美航空网络都是正相关的，但中国城市航空网络未表现出度度相关性；而对于度较大的节点，世界航空网络中其邻点平均度几乎是一个常值，但中国城市航空网络却呈现出负相关性.以往的实证研究暗示，节点具有明确几何位置的网络，如计算机互联网、电力网络等，不表现层次性.但是中国城市航空网络展现出明显的层次性，表明地理因素对其结构演化的影响并不强烈.进一步地，以城市间直航计划每周提供的座位数为边权，研究了网络的含权性质，发现该网络节点度权之间是幂律相关的，相关指数为1.37.     

复杂网络中心性对灾害蔓延的影响

基于一个普适性的灾害蔓延动力学模型,在三种网络拓扑结构(随机网、小世界网和无标度网)下,仿真分析了网络中心性对灾害蔓延速度和扩散趋势的影响.通过改变初始蔓延条件来分析网络初始状态对蔓延效率的影响,并着重讨论了在四种初始崩溃节点选取策略下灾害蔓延最终状态的差异.结果表明:对于四种攻击策略,网络最终状态有着明显的差异,网络对随机攻击具有较强的抵御能力,而对于目标,攻击却显示较强的脆弱性,或许,三种网络表现出不同的脆弱程度.最后,在一个实际网络上对理论分析结果进行了验证.     

基于复杂网络理论的北京公交网络拓扑性质分析

为分析公交复杂网络的拓扑性质, 本文以北京市为例, 选取截止到2010年7月的北京全市(14区、2县)的1165条公交线路和9618个公交站点为样本数据, 运用复杂网络理论构建起基于邻接站点的有向加权复杂网络模型. 该方法以公交站点作为节点, 相邻站点之间的公交线路作为边, 使得网络既具有复杂网络的拓扑性质同时节点(站点)又具有明确的地理坐标. 对网络中节点度、点强度、强度分布、平均最短路径、聚类系数等性质的分析显示, 公交复杂网络的度和点强度分布极为不均, 网络中前5%和前10%节点的累计强度分布分别达到22.43%和43.02%; 点强度与排列序数、累积强度分布都服从幂律分布, 具有无标度和小世界的网络特点, 少数关键节点在网络中发挥着重要的连接作用. 为分析复杂网络中的关键节点, 本文通过承载压力分析和基于"掠夺" 的区域中心节点提取两种方法, 得到了公交复杂网络中两类不同表现的关键节点. 这些规律也为优化城市公交网络及交通规划发展提供了新的参考建议.     

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.     

节点结构互异的复杂网络的时空混沌反同步

研究了节点结构互异的离散型时空混沌系统构成复杂网络的反同步问题. 通过构造合适的Lyapunov函数, 确定了复杂网络中连接节点之间的耦合函数的结构以及控制增益的取值范围. 以物理中具有时空混沌行为的激光相位共轭波空间扩展系统、Gibbs电光时空混沌 模型、Bragg声光时空混沌模型以及一维对流方程的离散形式作为 网络节点构成的复杂网络为例进行了仿真模拟, 发现整个网络存在稳定的混沌反同步现象.     

Impulsive synchronization of a nonlinear coupled complex network with a delay node

We investigate the impulsive synchronization of a nonlinear coupled complex network with a delay node.Both delay coupling and non-delay coupling,as well as the symmetrical coupling matrix and the asymmetrical coupling matrix are considered.Based on the comparison theorem of an impulsive differential system,some novel synchronization criteria are derived.Finally,numerical simulations demonstrate the effectiveness of the proposed synchronization criteria.     

一类节点结构互异的复杂网络的混沌同步

提出了一种实现节点结构互异的复杂网络的混沌同步方法.以异结构混沌系统作为节点构造复杂网络,基于Lyapunov稳定性定理确定了复杂网络中连接节点的耦合函数的形式.以Rssler系统、Coullet系统以及Lorenz系统作为网络节点构成的复杂网络为例,仿真模拟发现,整个复杂网络存在稳定的混沌同步现象.此方法不但可以实现任意混沌系统作为节点的网络混沌同步,而且网络节点数对整个复杂网络同步的稳定性也无影响,因而,具有一定的普适性. 关键词： 混沌同步 复杂网络 异结构 Lyapunov稳定性定理     

Impulsive synchronization of a nonlinear coupled complex network with a delay node

We investigate the impulsive synchronization of a nonlinear coupled complex network with a delay node. Both delay coupling and non-delay coupling, as well as the symmetrical coupling matrix and the asymmetrical coupling matrix are considered. Based on the comparison theorem of an impulsive differential system, some novel synchronization criteria are derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization criteria.     

Evolution of Chinese airport network

With the rapid development of the economy and the accelerated globalization process, the aviation industry plays a more and more critical role in today’s world, in both developed and developing countries. As the infrastructure of aviation industry, the airport network is one of the most important indicators of economic growth. In this paper, we investigate the evolution of the Chinese airport network (CAN) via complex network theory. It is found that although the topology of CAN has remained steady during the past few years, there are many dynamic switchings inside the network, which have changed the relative importance of airports and airlines. Moreover, we investigate the evolution of traffic flow (passengers and cargoes) on CAN. It is found that the traffic continues to grow in an exponential form and has evident seasonal fluctuations. We also found that cargo traffic and passenger traffic are positively related but the correlations are quite different for different kinds of cities.     

Analysis of the airport network of India as a complex weighted network

Transportation infrastructure of a country is one of the most important indicators of its economic growth. Here we study the Airport Network of India (ANI) which represents India’s domestic civil aviation infrastructure as a complex network. We find that ANI, a network of domestic airports connected by air links, is a small-world network characterized by a truncated power-law degree distribution and has a signature of hierarchy. We investigate ANI as a weighted network to explore its various properties and compare them with their topological counterparts. The traffic in ANI, as in the World-wide Airport Network (WAN), is found to be accumulated on interconnected groups of airports and is concentrated between large airports. In contrast to WAN, ANI is found to be having disassortative mixing which is offset by the traffic dynamics. The analysis indicates possible mechanism of formation of a national transportation network, which is different from that on a global scale.     

Projective synchronization of a complex network with different fractional order chaos nodes

Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this method, the projective synchronization of the network with different fractional order chaos nodes can be achieved, besides, the number of the nodes does not affect the stability of the whole network. In the numerical simulations, the chaotic fractional order Lü system, Liu system and Coullet system are chosen as examples to show the effectiveness of the scheme.     

随机扰动下时滞复杂动力网络的一致性

研究了随机扰动下一般时滞复杂动力网络的一致性问题,此复杂动力网络不仅具有随机扰动而且时变时滞同时出现在耦合项和节点系统中,所以这样的网络更具有一般性.基于随机Lyapunov稳定性理论、线性反馈控制理论和线性矩阵不等式,从理论上提出了此网络各个节点与孤立系统达到时滞无关和时滞相关一致性的充分条件.最后的数值模拟验证了理论结果的正确性和有效性.     

基于感知流量算法的复杂网络拥塞问题研究

研究了在具有感知流量的路由策略下,复杂网络的拓扑结构对网络中传输流量的影响.为了描述数据包传输过程的有效性,通过引入一个状态参数,利用由稳态到拥塞的指标流量相变值来刻画网络的吞吐量.基于每个节点的数据包处理能力与该节点的度或介数成比例提出两种模型并进行仿真.仿真结果表明,平均度相同的情况下,模型Ⅰ中,WS小世界网络比ER随机网络和BA无标度网络更容易产生拥塞;模型Ⅱ中,所有网络容量都得到较大的提高,尤其是WS小世界网络.但当网络的基本连接参数改变时,哪种模型更利于网络的流量传输,还要依据网络本身的结构特性 关键词： 复杂网络 无标度网络 感知流量 拥塞     

基于引力约束的复杂网络拥塞问题研究

如何在保证网络传输效率的同时提高网络的吞吐量是目前研究的主要问题. 通过研究节点对数据包传递过程的引力作用,提出了一种具有引力约束的路由算法. 为检验算法的有效性,通过引入一个状态参数H, 利用由稳态到拥塞状态的指标流量相变值来度量网络的吞吐量, 同时利用数据包的最大传输时间〈T_max〉 与平均传输时间 〈T_avg〉来分析网络的传输效率. 针对算法在不同引力约束条件下的路由情况进行了仿真.仿真结果表明, 若数据传递过程只考虑路径长度最短,则会导致网络吞吐量较低且流量分布极不均匀; 若只顾及等待时间最短,会导致传输路径过度迂回且大部分节点都会陷入拥塞状态; 同时考虑路径长度和等待时间的引力作用并选取适当引力的节点进行传递, 可以显著提高网络吞吐量并缓解网络的拥塞程度.