Open AccessApplication of a fractional algorithm to studying the competition between dissipation and fluctuation in non-Markov process
Author(s) -
Lin Fang,
Hu Dan-Qing,
Lele Li
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.120503
Subject(s) - dissipation , statistical physics , markov process , markov chain , random walk , physics , diffusion , variable (mathematics) , langevin equation , stochastic process , competition (biology) , mathematics , mathematical analysis , quantum mechanics , statistics , ecology , biology
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.