含权复杂网络模型及其动力学-控制理论与控制工程专业论文.docxVIP

AbstractIn Abstract In this paper weighted complex a network modeling iS discussed from two different perspectives，as well as a new type of synchronization in weighted complex networks is proposed．Firstly，we propose the growth of weighted complex networks driven by traffic flow in networks，after analyzing the empirical results of weighted networks， establishing a model which can realize many statistical characteristics observed in real．world network，such as power．1aw distribution of node degree，node strength and link weight，explicating the possible cause of disassortative mixing in technical networks． All this effectively solves the defects in previous weighted complex networks modeling．Secondly, in order to explicate the root of power-law function between strength and degree in weighted networks．another modeling iS proposed based network flow of kinetic equilibrium，which not only analyze the root of nonlinear correlation between strength and degree but also produce approach to weigh network of given infrastructure．In the end part of the thesis，a new synchronization approach iS mentioned，a model which the previous models and more accurately describe the synchronization phenomena in the real—world．To sum up，the three researches make much significance when it comes to building up more efficient，more reliable networks，such Intemet，transportation networks and power grids． Key words：Complex networks，Weighted networks，Power-law distribution，Synchronization 第一章复杂网络的概述这一章我们给出了复杂网络的背景，它的研究历史，阻及复杂网络的特性， 第一章复杂网络的概述 这一章我们给出了复杂网络的背景，它的研究历史，阻及复杂网络的特性， 分类等等，同时在晟后我们指出了含权复杂网络研究的意义，蛆及我们的主要研 究内容和成果。 1．1复杂网络的发现与研究 网络可以被看成由结点和连边构成，其中结点可以看成是由系统中的各种元 件的一种抽象，而连边可以看成是元件之间的相互作用和关系 。网络采用这 种数学形式实际上大量的存在于自然界中，如Internet网络，www网络，个人 之间的人际关系网络(节点之间的连边表示他们互相认识)『2-4]， 再有就是商 业网络，公司网络，神经网络，食物链网络f5—7]，分配网络如人身体内的血管构 成的网络，邮递网络，演员合作网络，科学家合作网络等等f8。91。 网络的研究传统上属于图论的范畴。以圈论【10．12】为基础的网络研究构成网 络研究的重要基石，特别是自欧拉解决七桥问题以来，这门学科己发展成一个较 完备的知识体系。早期的网络研究主要集中在小规摸的规则网络上。1959．1961 年，匈牙利科学家Erdos和Reny(ER)提出了著名的随机网络模型[13．14]，它具