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Efficiency-Controllable Random Walks on a Class of Recursive Scale-Free Trees with a Deep Trap |
| LI Ling1,2**, GUAN Ji-Hong1**, ZHOU Shui-Geng3,4 |
1Department of Computer Science and Technology, Tongji University, Shanghai 201804
2Department of Basic Courses, Zhejiang Shuren University, Hangzhou 310015
3School of Computer Science, Fudan University, Shanghai 200433
4Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai 200433
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| Cite this article: |
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LI Ling, GUAN Ji-Hong, ZHOU Shui-Geng 2015 Chin. Phys. Lett. 32 030501 |
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Abstract Controls, especially efficiency controls on dynamical processes, have become major challenges in many complex systems. We study an important dynamical process, random walk, due to its wide range of applications for modeling the transporting or searching process. For lack of control methods for random walks in various structures, a control technique is presented for a class of weighted treelike scale-free networks with a deep trap at a hub node. The weighted networks are obtained from original models by introducing a weight parameter. We compute analytically the mean first passage time (MFPT) as an indicator for quantitatively measuring the efficiency of the random walk process. The results show that the MFPT increases exponentially with the network size, and the exponent varies with the weight parameter. The MFPT, therefore, can be controlled by the weight parameter to behave superlinearly, linearly, or sublinearly with the system size. This work provides further useful insights into controlling efficiency in scale-free complex networks.
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Published: 26 February 2015
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| PACS: |
05.40.Fb
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(Random walks and Levy flights)
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05.60.Cd
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(Classical transport)
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89.75.Hc
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(Networks and genealogical trees)
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89.75.Da
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(Systems obeying scaling laws)
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[1] Boccaletti S et al 2006 Phys. Rep. 424 175
[2] Dorogovtsev S N et al 2008 Rev. Mod. Phys. 80 1275
[3] Liu Y Y et al 2011 Nature 473 167
[4] Yuan Z Z et al 2013 Nat. Commun. 4 2447
[5] Liu Y Y et al 2012 PLoS ONE 7 e44459
[6] Yan G et al 2012 Phys. Rev. Lett. 108 218703
[7] Nepusz T and Vicsek T 2012 Nat. Phys. 8 568
[8] Wang W X et al 2006 Phys. Rev. E 73 026111
[9] Ou Q et al 2007 Phys. Rev. E 75 021102
[10] Kim B J et al 2002 Phys. Rev. E 65 027103
[11] Jiang B et al 2009 Phys. Rev. E 80 021136
[12] Hughes R D 1995 Random Walks Random Environments (Oxford: Clarendon)
[13] Metzler R and Klafter J 2000 Phys. Rep. 339 1
[14] Metzler R and Klafter J 2004 J. Phys. A 37 R161
[15] Burioni R and Cassi D 2005 J. Phys. A 38 R45
[16] Hwang S et al 2012 Phys. Rev. Lett. 109 088701
[17] Hwang S et al 2012 Phys. Rev. E 85 046110
[18] Bénichou O et al 2011 Rev. Mod. Phys. 83 81
[19] Fouss F et al 2007 IEEE Trans. Knowl. Data Eng. 19 355
[20] Condamin S et al 2007 Nature 450 77
[21] Condamin S et al 2008 Proc. Natl. Acad. Sci. USA 105 5675
[22] Lloyd A L and May R M 2001 Science 292 1316
[23] Bar-Haim A, Klafter J and Kopelman R 1997 J. Am. Chem. Soc. 119 6197
[24] Bar-Haim A and Klafter J 1998 J. Phys. Chem. B 102 1662
[25] Agliari E 2011 Physica A 390 1853
[26] Montroll E W 1969 J. Math. Phys. 10 753
[27] Noh J D and Rieger H 2004 Phys. Rev. Lett. 92 118701
[28] Garza-López R A and Kozak J J 2005 Chem. Phys. Lett. 406 38
[29] Li L, Guan J H and Zhou S G 2014 Physica A 415 463
[30] Bentz J L, Turner J W and Kozak J J 2010 Phys. Rev. E 82 011137
[31] Wu B, Lin Y, Zhang Z Z and Chen G R 2012 J. Chem. Phys. 137 044903
[32] Lin Y and Zhang Z Z 2013 J. Chem. Phys. 138 094905
[33] Agliari E 2008 Phys. Rev. E 77 011128
[34] Haynes C P and Roberts A P 2008 Phys. Rev. E 78 041111
[35] Lin Y, Wu B and Zhang Z Z 2010 Phys. Rev. E 82 031140
[36] Zhang Z Z, Wu B and Chen G R 2011 Europhys. Lett. 96 40009
[37] Zhang Z Z, Xie W L, Zhou S G, Li M and Guan J H 2009 Phys. Rev. E 80 061111
[38] Zhang Z Z, Qi Y, Zhou S G, Xie W L and Guan J H 2009 Phys. Rev. E 79 021127
[39] Tejedor V, Bénichou O and Voituriez R 2009 Phys. Rev. E 80 065104(R)
[40] Zhang Z Z, Yang Y H and Gao S Y 2011 Eur. Phys. J. B 84 331
[41] Zhang Z Z, Lin Y, Gao S Y, Zhou S G, Guan J H and Li M 2009 Phys. Rev. E 80 051120
[42] Zhang Z Z, Zhou S G, Xie W L, Chen L C, Lin Y and Guan J H 2009 Phys. Rev. E 79 061113
[43] Zhang Z Z, Yang Y H and Lin Y 2012 Phys. Rev. E 85 011106
[44] Yang Y H and Zhang Z Z 2013 J. Chem. Phys. 139 234106
[45] Bar-Haim A and Klafter J 1998 J. Chem. Phys. 109 5187
[46] Wu B and Zhang Z Z 2013 J. Chem. Phys. 139 024106
[47] Ravasz E, Somera A L, Mongru D A, Oltvai Z N and Barabási A L 2002 Science 297 1551
[48] Ravasz E and Barabási A L 2003 Phys. Rev. E 67 026112
[49] Andrade Jr J S, Herrmann H J, Andrade R F and Da Silva L R 2005 Phys. Rev. Lett. 94 018702
[50] Zhou T, Yan G and Wang B H 2005 Phys. Rev. E 71 046141
[51] Carletti T and Righi T 2010 Physica A 389 2134
[52] Jung S, Kim S and Kahng B 2002 Phys. Rev. E 65 056101
[53] Comellas F, Rozenfeld H D and Ben-Avraham D 2005 Phys. Rev. E 72 046142
[54] Dorogovtsev S N, Mendes J F F and Oliveira J G 2006 Phys. Rev. E 73 056122
[55] Zhang Z Z, Lin Y and Ma Y J 2011 J. Phys. A 44 075102
[56] Zhang Z Z, Zhang Y C, Zhou S G, Yin M and Guan J H 2009 J. Math. Phys. 50 033514
[57] Barrat A, Barthélemy M and Vespignani A 2004 Phys. Rev. Lett. 92 228701
[58] Wu A C, Xu X J, Wu Z X and Wang Y H 2007 Chin. Phys. Lett. 24 577
[59] Fronczak A and Fronczak P 2009 Phys. Rev. E 80 016107
[60] Zhang Z Z, Shan T and Chen G R 2013 Phys. Rev. E 87 012112
[61] Bollt E and Ben-Avraham D 2005 New J. Phys. 7 26 |
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