一类推广的择优增长系统的度分布

Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (5): 977-983.

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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.

Abstract

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

CLC Number:

05C80

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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Degree Distribution of a Promoted Preferential Growth System

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