Application of a fractional algorithm to studying the competition between dissipation and fluctuation in non-Markov process

Abstract

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.