一类推广的择优增长系统的度分布

数学物理学报 ›› 2013, Vol. 33 ›› Issue (5): 977-983.

一类推广的择优增长系统的度分布

康宁|荆科*|侯振挺

阜阳师范学院经济与管理学院安徽阜阳 236037；阜阳师范学院数学与计算科学学院安徽阜阳 236037；中南大学数学与统计学院长沙 410075

收稿日期:2012-03-19 修回日期:2013-04-22 出版日期:2013-10-25 发布日期:2013-10-25
通讯作者: 荆科，jingxuefei296@sina.com E-mail:jingxuefei296@sina.com; kangningning2006@126.com
基金资助:
国家特色专业数学与应用数学(TS11496)、安徽省高等学校省级教学质量与教学改革工程重点项目(20101984)、安徽省高等学校省级自然科学研究项目(KJ2013Z268)、数学天元基金(11226200)和阜阳师范学院自然科学基金(2013FSKJ11)资助.

Degree Distribution of a Promoted Preferential Growth System

KANG Ning, JING Ke*, HOU Zhen-Ting

School of Economic and Management, Fuyang Teachers College, Anhui Fuyang 236037；School of Mathematics and Computational Science, Fuyang Teachers College, Anhui Fuyang 236037；School of Mathematics Sciences and Computing Technology, Central South University, Hunan Changsha 410075

Received:2012-03-19 Revised:2013-04-22 Online:2013-10-25 Published:2013-10-25
Contact: JING Ke，jingxuefei296@sina.com E-mail:jingxuefei296@sina.com; kangningning2006@126.com
Supported by:
国家特色专业数学与应用数学(TS11496)、安徽省高等学校省级教学质量与教学改革工程重点项目(20101984)、安徽省高等学校省级自然科学研究项目(KJ2013Z268)、数学天元基金(11226200)和阜阳师范学院自然科学基金(2013FSKJ11)资助.

摘要/Abstract

摘要：

研究文献[1]中提出的一类择优增长系统, 将模型推广至成员成批到达的情形, 经每时间步, 系统中分别增加一个团体和m个成员. 这m个成员相互独立的依概率p加入旧团体, 加入旧团体的概率与旧团体中的成员数成正比; 依概率q=1-p加入新团体. 该文利用马氏链方法严格证明系统度分布的存在性, 并给出其精确解, 从而得出该系统为无标度系统.

关键词: 择优增长系统, 度分布, 无标度性, 马氏链

Abstract:

We study a class of preferential growth system [1] and promote the model to a general situation. Considering there are m elements added to the system at each time step, The m elements can either join in the new group (with probability q=1-p) or dependently join in an already existing group with a probability proportional to the size thereof. Based on the Markov chain theory, we get the rigorous proof for the existence of the steady-state degree distribution and obtain the exact solution, then prove the model has scale-free property.

Key words: Preferential growth system, Steady-state degree distribution, Scale-free property, Markov chain

中图分类号:

05C80

康宁, 荆科, 侯振挺. 一类推广的择优增长系统的度分布[J]. 数学物理学报, 2013, 33(5): 977-983.

KANG Ning, JING Ke, HOU Zhen-Ting. Degree Distribution of a Promoted Preferential Growth System[J]. Acta mathematica scientia,Series A, 2013, 33(5): 977-983.

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