对一些复杂网络的统计描述与性质的研究

【作者】 许田；

【导师】 何大韧；

【作者基本信息】 扬州大学 ， 凝聚态物理， 2004， 硕士

【摘要】 复杂网络描述了广泛多样的高科技系统，例如：化学反应网络、因特网、社会网络、WWW网等等。研究这些复杂网络是为了弄清产生它们的内在机制，了解他们的演化规律，进而找到这些网络至上的复杂运行过程与网络结构的关系，以便积累对支配复杂系统的自然规律的认识。本文报导我们在复杂网络研究中的一些体会。第一章是绪论，所做工作集中在第二至第六章。 第二章分别提出了演员合作网络和科研合作网络的双粒子图自适应发展模型。模型考虑作用者采取的选择、决策、竞争以及由此导致的自身和整个网络的进化。对模型的数值模拟所得到的结果与实际的统计结果很好地符合，说明自适应复杂网络可以自组织向小世界、无标度的结构。本文也讨论了双粒子图的不同投影单粒子图模拟所得结果的异同，以及提出了一个顶点团簇度的概念。 第三章报道我们统计得到的、中国电力网所具有的符合已知的网络共性的性质，以及基于这些共性所提出的一个可能在粗糙程度上再现中国电力网发展历程的动力学模型。这种对电力网极其简化的描述思路也许可能给电力网建模的研究一些启示。 第四章报道我们得到的长江河流网络的统计性质，以及长江流域各个港口之间航运和贸易的统计性质，以及描述这个航运和贸易网络的一个复杂自适应模型。根据此模型模拟了各港口城市经济发展机制和互相之间的贸易竞争，并把模拟结果与统计数据作了对比。 第五章提出了一个新的统计参数——成功合作度Cr。目的是为了把复杂网的结构和工作特性联系起来。在本章中报道了我们数值计算所得到的演员合作网络和科研合作网络的Cr参数分布规律，以及Cr参数在一个“专门为了研究电网的大停电雪崩过程所提出的”最简化电力网模型中反映的复杂网的结构和感兴趣的工作特性——鲁棒性和敏感性之间的关系。 第六章从一个角度讨论流行病传播模型的发展历史，认为主要经历了决定论模型、原胞自动机模型和复杂网络模型这三个阶段，同时简要介绍了本课题组和扬州人’学硕!一学位沦义其他课题组分别运用决定论模型、原胞自动机模型或复杂网络模型模拟一1匕京门川勺抓I{S传播过程的一些例子，以图说明这扭个阶段中取得的认识进展都有利j飞对熟邓传播建立模型、进行预测、探讨规律，然而不同的模型又各具特点。在父杂网络模型模拟的介绍中重点叙述近年来的重要认识，即网络的“小山.界性”、“无标度性”、“高团簇性”对流行病传播的影l响，少补月_报道了木课题到叮卜模拟SAI{S传播时得到的相应结果。更多还原

【Abstract】 Complex networks describe a wide variety of high technological systems. For example, the network of chemical reactions, Internet network, social network, the World Wide Web and so on. The aim of the studies on these networks is to investigate their mechanisms, understand their developing rules, and find the relationship between their structure and the complex functioning processes on them, so as to accumulate the knowledge about the natural disciplinarians dominating the complex systems. This thesis reports some realizations in our complex network’s research. The first chapter is an introduction part, and most of our works are described in chapters 2 to 6.The second chapter suggests a self-adaptive bi-particle graph model, which describes the collaboration network between film actors or the principal investigators and their assistants. The model considers the choices, strategies, competitions, and the induced evolutions of the scientists or film actors and as well as the evolution of the whole network. The simulation results of all the different single-particle graphs obtained by different methods of projection show a good agreement with the statistical data. That shows a self-adaptive complex network can self-organize to a small world and scale-free structure. This article also discusses the similarities and differences of the simulation results of the different projected single-particle graphs of the bi-particle graph.The third chapter reports the properties of Chinese power grid those we have statistically observed. The properties show a good agreement with the universal ones. We also present a dynamical model, which may reproduce the developing process of Chinese power grid in the coarseness. This very simplified description idea for the power grid may give a kind of elicitation to the scientists who study the models of power grid.The forth chapter reports some statistical properties of river network of Yangtze as well as the statistical properties of shipping and commerce between the ports along theriver. In the chapter we also suggest a complex self-adaptive model that describe the shipping and commerce network. A computer simulation on the development mechanism and commercial competitions of the ports has been performed. The simulation results are compared with the statistical data.In the fifth chapter we define a new parameter, the successful collaboration ration (Cr). It is our wish that the parameter can connect the structure of complex networks and their working characteristics. We report the distribution rules of Cr parameter in the collaboration network between film actors or the principal investigators and their assistants. Also, the relationship between structure of a simplified complex network model and the interesting working properties, the tolerance and sensitivity, has been reported. The model is constructed for a study on the avalanches in the power grids.The last chapter presents, from a view of point, a discussion on the development history of the models of epidemic spreading. We suggest that it can be divided into three stages: deterministic models, cellular automata models, and complex network models. We briefly introduce some samples of the simulation on the process of SARS spreading in Beijing by means of deterministic models, cellular automata models, and complex network models, respectively, conducted by our group or other groups, so as to show that all the achievements in the three stages are helpful for establishing models, performing forecasting and searching for rules of SARS spreading, but different models have different characteristics. In the introduction of the simulation with complex network models we emphasize the important achievements in the recent studies, which are the influences of the small world characteristic, the scaling-free characteristic and the high-clustering characteristic of the network on the epidemic spreading. We also report the results obtained by our group in the simulation of SARS spreading those correspond to the achievements.更多还原