【作者】 崔迪；

【导师】 高自友；

【作者基本信息】 北京交通大学 ， 系统分析与集成， 2009， 博士

【摘要】 近几年,复杂网络的研究受到国内外学者的广泛关注。复杂网络的研究方法为研究系统的复杂性提供了新视角和新方法。小世界效应与无标度特性的科学发现掀起了对复杂网络结构及其动力学特性的研究热潮,提高了人们对现实世界的科学认识。随着研究的深入,对于复杂网络的探讨已经渗透到社会学、生物学、物理学、经济学、计算机科学以及交通运输等各研究领域中。很多大型的复杂网络都呈现出一种特性——群落结构。也就是说:整个网络由若干个群落结构所组成,每个群落结构内部节点之间的连接相对比较紧密,但各个群落结构之间连接相对比较稀疏。研究这些网络不仅对人们的工作和生活具有重要的现实意义,而且对人类了解自然界和生物系统具有深远的科学意义。本论文主要研究了带有群落结构的复杂网络上的级联失效行为和流量特性,研究工作和创新点主要有如下几个方面:(1)基于耦合映象格子方法研究带有群落结构的小世界网络和无标度网络上的节点的级联失效行为。先后研究了群落结构的平均度、群落结构的重连概率对于级联失效过程中失效节点数的影响。重点研究基于四种不同的攻击策略下,外部干扰、失效的节点数以及群落结构的模块度对级联失效行为的影响。最后考虑了外部干扰服从正态分布的情况下,通过正态分布的均值和方差分别表示外部干扰的强弱和波动,从而研究外部干扰对复杂网络中的边的级联失效行为所产生的影响。(2)基于网络均衡配流模型研究带有群落结构的复杂网络中的流量特性。基于三种网络均衡配流模型研究带有群落结构的复杂网络上的拥挤程度和效率,分析和研究了OD需求和群落结构的模块度的影响。(3)提出并研究了一个带有群落结构的非对称演化网络模型。应用平均场理论进行近似分析,并通过数值模拟进行验证,发现该模型的效用分布具有一定的幂律特性,而度分布在连接概率较小时,具有指数衰减的特性;而在连接概率较大时,具有幂律分布的特性。更多还原

【Abstract】 In recent years, the research of complex network has been received a wide range concerns by scholars at home and abroad. The research methods of complex networks have been provided a new perspective and new approach for studying the complexity of the systems. The finding of small-world effects and scale-free property has attracted a great deal of attention of complex networks structure and dynamics, which raise the science awareness for the real world. With the in-depth research for complex networks, it has infiltrated including sociology, biology, physics, economics, computer science, as well as transport and other areas. Many large-scale complex networks has emerged a common characteristic the community structure. That is to say, the entire networks are constituted by a number of community structures. The connection of inner-community is relatively close. At the same time, the connection of inter-community is quite sparse.Research on these networks has the vital practical significance for the people’s works and life. Moreover, understanding the nature and biological systems has the profound scientific significance for human. This dissertation mainly studies the cascading failure process and flow characteristics based on the community structure, the main content of this dissertation and innovation are summarized as following:(1) Firstly, cascading failures are studied by the coupled map lattices methods in the small-world networks with community structure and scale-free networks with community structure. The close relationships of the modularity, the external perturbation, the mean degree, the number of failed nodes, the different rewiring probabilities, external perturbation and the four different attack strategies are shown. Finally, the external perturbation can be burden by community networks while the different external perturbations attribute the normal distribution with the different the mean value and the variance.(2) Secondly, combining the user equilibrium, system optimization and system equilibrium assignment with complex networks theory, the congested effects of flow in complex networks is studied. The close relationships of the OD flows, modularity and congested effects are studied based on the community structure in small-world networks and the scale-free networks.(3) Thirdly, the simple asymmetrically evolved community networks with a combination of preferential attachment and random properties are proposed. The simulation results show that the model can reproduce a power-law utility distribution, which can be obtained by using the mean-field approximation methods. And its degree distribution is attributed to the power-law dictribution with the high probabilities and it is followed the exponent distribution with the low probabilities.更多还原