摘要
介绍近年来复杂网络研究中常用的几种统计物理学方法(平均场理论、主方程、率方程、生成函数)的物理背景、发展历史、观点、思想和方法.回顾了物理学在研究连续相变、自组织临界现象、流行病传播等问题时是如何发展、运用平均场理论,以及平均场理论的思想、方法在从平衡态向非平衡态研究的延伸过程中的演化过程.简介了主方程、率方程和生成函数的相关物理思想和概念.在最后一节介绍了一些运用这些方法研究复杂网络的成果,包括一些最著名以及值得注意的网络演化模型的平均场方法、主方程和率方程方法求解,一些网络统计性质的解析求解,以及一些网络上物理过程特征描述的解析分析等.
This paper presents the physics backgrounds, history of development, viewpoints and methods of some statistical physics methods recently used in complex network investigations （mean field theory, master equation, rate equation, and generating function）. We reviewed how the mean field theory was developed and used in the studies of continuous phase transition, self-organized criticality and epidemics, and how the mean field theory ideas and methods evolved in the transition from equilibrium to non-equilibrium studies. The corresponding physics ideas and methods of master equation, rate equation, and generating function are first presented, and some complex network research achievements obtained by using the methods are reviewed in the last section, such as using mean field methods, master equation and rate equation to solve the most famous and other noticeable network evolution models, to solve some network statistical properties and to analyze the characteristic descriptions of some network physical processes.
出处
《力学进展》
EI
CSCD
北大核心
2008年第6期692-701,共10页
Advances in Mechanics
基金
国家自然科学基金重点基金(10635040)资助项目~~
关键词
复杂网络
统计物理学
平均场近似
生成函数
complex network, statistical physics, mean field approximation, generating function
