中国物理B ›› 2012, Vol. 21 ›› Issue (3): 38901-038901.doi: 10.1088/1674-1056/21/3/038901

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张静远1,孙伟刚1,陈关荣2   

  • 收稿日期:2011-11-13 修回日期:2011-12-09 出版日期:2012-02-15 发布日期:2012-02-15
  • 通讯作者: 孙伟刚,wgsun999@yahoo.com.cn E-mail:wgsun999@yahoo.com.cn

Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap

Zhang Jing-Yuan(张静远)a), Sun Wei-Gang(孙伟刚) a)†, and Chen Guan-Rong(陈关荣)b)   

  1. a. School of Science, Hangzhou Dianzi University, Hangzhou 310018, China;
    b. Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, China
  • Received:2011-11-13 Revised:2011-12-09 Online:2012-02-15 Published:2012-02-15
  • Contact: Sun Wei-Gang,wgsun999@yahoo.com.cn E-mail:wgsun999@yahoo.com.cn
  • Supported by:
    Project supported by the Research Foundation of Hangzhou Dianzi University, China (Grant Nos. KYF075610032 and zx100204004-7) and the Hong Kong Research Grants Council, China (Grant No. CityU 1114/11E).

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Abstract: In this paper, we study the scaling for the mean first-passage time (MFPT) of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from a triangle to a polygon, we obtain the exact scaling for the MFPT. We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order. In addition, we determine the exponents of scaling efficiency characterizing the random walks. Our results are the generalizations of those derived for the Koch network, which shed light on the analysis of random walks over various fractal networks.

Key words: mean first-passage time, random walks, Koch networks

中图分类号:  (Networks and genealogical trees)

  • 89.75.Hc
05.40.Fb (Random walks and Levy flights) 05.10.-a (Computational methods in statistical physics and nonlinear dynamics)