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Based on fractional Langevin equation and random walk theory, a numerical algorithm that can be applied to non-Markov long-memory system is established in this paper. In addition, the evolution behaviour of random variable ruled by fractional sub-diffusion equation is numerically studied in three conditions: no dissipation, no fluctuation and both being present. The results show that competition exists between dissipation and fluctuation. As time goes by, the effect of Guassian fluctuation weakens and damping plays a main role in the evolution of system; however, because of the existance of "rare-though-dominant" events, long-tail fluctuation makes the evolution of system abrupt change at a certain probability.
[1] Metzler R, Klafter J 2000 Phys. Rep. 339 1
[2] Bao J D 2012 Introduction of Anomalous Statistical Dynamics (Science Press, Beijing) (in Chinese) [包景东 2012 反常统计动力学导论 (北京: 科学出版社)]
[3] Richardson L F 1926 Proc. Roy. Soc. 110 709
[4] Bao J D 2005 Prog. Phys. 25 359 (in Chinese) [包景东 2005 物理学进展 25 359]
[5] Bao J D, Zhou Y Z 2003 Phys. Rev. Lett. 91 138104
[6] Fogedby H C 1994 Phys. Rev. Lett. 73 2517
[7] Chechkin A V, Gonchar V Yu 2000 Physica A 277 312
[8] Beran J 1994 Statistics of Long-Memory Process (New York: Chapman and Hall)
[9] L K, Bao J D 2005 Phys. Rev. E 72 067701
[10] Bao J D, Zhou Y Z, L K 2006 Phys. Rev. E 74 041125
[11] Lutz E 2010 Phys. Rev. E 64 051106
[12] Einstein A 1905 Ann. Phys. (Leipzig) 17 549
[13] Pearson K 1905 Nature 72 342
[14] Montroll E W, Weiss G H 1965 J. Math. Phys. 6 167
[15] Scher H, Montroll E W 1975 Phys. Rev. B 12 2455
[16] Bouchaud J P, Georges A 1990 Phys. Rep. 195 12
[17] West B J 1999 Physiology, Promiscuity and Prophecy at the Millennium: A Tale of Tails (Singapore: World Scientific)
[18] Hosking J T M 1981 Biometrika 68 165
[19] Burov S, Barkai E 2008 Phys. Rev. Lett. 100 070601
[20] Burov S, Barkai E 2008 Phys. Rev. E 78 031112
[21] Lin F, Bao J D 2011 Chin. Phys. B 20 040502
[22] Heinsalu E, Patriarca M, Goychuk I, Hänggi P 2007 J. Phys.: Condens. Matter 19 065114
[23] Dybiec B 2009 Phys. Rev. E 80 041111
[24] L Y, Bao J D 2011 Phys. Rev. E 84 051108
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[1] Metzler R, Klafter J 2000 Phys. Rep. 339 1
[2] Bao J D 2012 Introduction of Anomalous Statistical Dynamics (Science Press, Beijing) (in Chinese) [包景东 2012 反常统计动力学导论 (北京: 科学出版社)]
[3] Richardson L F 1926 Proc. Roy. Soc. 110 709
[4] Bao J D 2005 Prog. Phys. 25 359 (in Chinese) [包景东 2005 物理学进展 25 359]
[5] Bao J D, Zhou Y Z 2003 Phys. Rev. Lett. 91 138104
[6] Fogedby H C 1994 Phys. Rev. Lett. 73 2517
[7] Chechkin A V, Gonchar V Yu 2000 Physica A 277 312
[8] Beran J 1994 Statistics of Long-Memory Process (New York: Chapman and Hall)
[9] L K, Bao J D 2005 Phys. Rev. E 72 067701
[10] Bao J D, Zhou Y Z, L K 2006 Phys. Rev. E 74 041125
[11] Lutz E 2010 Phys. Rev. E 64 051106
[12] Einstein A 1905 Ann. Phys. (Leipzig) 17 549
[13] Pearson K 1905 Nature 72 342
[14] Montroll E W, Weiss G H 1965 J. Math. Phys. 6 167
[15] Scher H, Montroll E W 1975 Phys. Rev. B 12 2455
[16] Bouchaud J P, Georges A 1990 Phys. Rep. 195 12
[17] West B J 1999 Physiology, Promiscuity and Prophecy at the Millennium: A Tale of Tails (Singapore: World Scientific)
[18] Hosking J T M 1981 Biometrika 68 165
[19] Burov S, Barkai E 2008 Phys. Rev. Lett. 100 070601
[20] Burov S, Barkai E 2008 Phys. Rev. E 78 031112
[21] Lin F, Bao J D 2011 Chin. Phys. B 20 040502
[22] Heinsalu E, Patriarca M, Goychuk I, Hänggi P 2007 J. Phys.: Condens. Matter 19 065114
[23] Dybiec B 2009 Phys. Rev. E 80 041111
[24] L Y, Bao J D 2011 Phys. Rev. E 84 051108
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