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

doi:10.1088/1674-1056/21/3/038901

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.

Keywords: mean first-passage time random walks Koch networks

Received: 13 November 2011
Revised: 09 December 2011
Accepted manuscript online:

PACS:	89.75.Hc	(Networks and genealogical trees)
	05.40.Fb	(Random walks and Levy flights)
	05.10.-a	(Computational methods in statistical physics and nonlinear dynamics)

Fund: 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).

Corresponding Authors: Sun Wei-Gang,wgsun999@yahoo.com.cn
E-mail: wgsun999@yahoo.com.cn

Cite this article:

Zhang Jing-Yuan(张静远), Sun Wei-Gang(孙伟刚), and Chen Guan-Rong(陈关荣) Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap 2012 Chin. Phys. B 21 038901

[1] Comellas F, Oz髇 J and Peters J G 2000 Inf. Process. Lett. 76 83
[2] Barab醩i A L, Ravasz E and Vicsek T 2001 Phys. A 299 559
[3] Dorogovtsev S N and Mendes J F F 2002 Adv. Phys. 51 1079
[4] Song C, Havlin S and Makse H A 2005 Nature 433 392
[5] Goh K I, Salvi G, Kahng B and Kim D 2006 Phys. Rev. Lett. 96 018701
[6] Doye J P K and Massen C P 2005 Phys. Rev. E 71 016128
[7] Wu J J, Gao Z Y and Sun H J 2007 Chin. Phys. 16 47
[8] Qian J H, Han D D and Ma Y G 2011 Acta. Phys. Sin. 60 098901 (in Chinese)
[9] Zhang J Y and Sun W G 2010 J. Stat. Mech. P07011
[10] Sun W G, Zhang J Y and Wu Y Q 2011 J. Stat. Mech. P03021
[11] Liu J X and Kong X M 2010 Acta. Phys. Sin. 59 2244 (in Chinese)
[12] Zhang Z Z, Gao S Y, Chen L C, Zhou S G, Zhang H J and Guan J H 2010 J. Phys. A: Math. Theor. 43 395101
[13] Zhang Z Z, Wu B, Zhang H J, Zhou S G, Guan J H and Wang Z G 2010 Phys. Rev. E 81 031118
[14] Sun W G, Wu Y Q, Chen G R and Wang Q Y 2011 J. Stat. Mech. P10032
[15] Watts D J and Strogatz S H 1998 Nature 393 440
[16] Barab醩i A L and Albert R 1999 Science 286 509
[17] Bollt E M and Avraham D 2005 New J. Phys. 7 26
[18] Burioni R and Cassi D 2005 J. Phys. A: Math. Gen. 38 R45
[19] Condamin S, B閚ichou O, Tejedor V, Voituriez R and Klafter J 2007 Nature 450 77
[20] Agliari E and Burioni R 2009 Phys. Rev. E 80 031125
[21] Zhang Z Z, Zhou S G, Xie W L, Chen L C, Lin Y and Guan J H 2009 it Phys. Rev. E 79 061113
[22] Comellas F and Miralles A 2010 Phys. Rev. E 81 061103
[23] Reuveni S, Granek R and Klafter J 2010 Phys. Rev. E 82 041132
[24] Tejedor V, B閚ichou O, Voituriez R and Moreau M 2010 Phys. Rev. E 82 056106

[1]	Nodes and layers PageRank centrality for multilayer networks Lai-Shui Lv(吕来水), Kun Zhang(张琨), Ting Zhang(张婷), Meng-Yue Ma(麻孟越). Chin. Phys. B, 2019, 28(2): 020501.
[2]	Diffusional inhomogeneity in cell cultures Jia-Zheng Zhang(张佳政), Na Li(李娜), Wei Chen(陈唯). Chin. Phys. B, 2018, 27(2): 028705.
[3]	Rotational stretched exponential relaxation in random trap-barrier model Ekrem Aydıner. Chin. Phys. B, 2015, 24(7): 070501.
[4]	Random walks in generalized delayed recursive trees Sun Wei-Gang (孙伟刚), Zhang Jing-Yuan (张静远), Chen Guan-Rong (陈关荣). Chin. Phys. B, 2013, 22(10): 108904.
[5]	Enhancement of density divergence in an insect outbreak model driven by colored noise Xiao Rong (肖荣), Wang Can-Jun (王参军), Zhang Lin (张林 ). Chin. Phys. B, 2012, 21(11): 110504.
[6]	Energy diffusion controlled reaction rate in dissipative Hamiltonian systems Deng Mao-Lin(邓茂林) and Zhu Wei-Qiu(朱位秋). Chin. Phys. B, 2007, 16(6): 1510-1515.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention