Universality classes of fluctuation dynamics in hierarchical complex systems

摘要

A unified approach is proposed to describe the statistics of the short-time dynamics of multiscale complexsystems. The probability density function of the relevant time series (signal) is represented as a statisticalsuperposition of a large time-scale distribution weighted by the distribution of certain internal variables thatcharacterize the slowly changing background. The dynamics of the background is formulated as a hierarchicalstochastic model whose form is derived from simple physical constraints, which in turn restrict the dynamicsto only two possible classes. The probability distributions of both the signal and the background have simplerepresentations in terms ofMeijerGfunctions. The two universality classes for the background dynamics manifestthemselves in the signal distribution as two types of tails: power law and stretched exponential, respectively. Adetailed analysis of empirical data from classical turbulence and financial markets shows excellent agreementwith the theory.