Dynamical modelling of superstatistical complex systems

TL;DR

This paper develops a method to construct optimal superstatistical dynamical models from experimental time series, demonstrated on turbulent flow data, enabling better understanding of complex systems' dynamics.

Contribution

It generalizes the superstatistics concept to include Langevin equations with fluctuating memory kernel parameters, allowing for synthetic models matching experimental data.

Findings

Successfully modeled turbulent velocity data with superstatistical Langevin equations.

Provided a systematic way to construct models with the same invariant density and correlation functions.

Applicable to various complex systems beyond turbulence.

Abstract

We show how to construct the optimum superstatistical dynamical model for a given experimentally measured time series. For this purpose we generalise the superstatistics concept and study a Langevin equation with a memory kernel whose parameters fluctuate on a large time scale. It is shown how to construct a synthetic dynamical model with the same invariant density and correlation function as the experimental data. As a main example we apply our method to velocity time series measured in high-Reynolds number turbulent Taylor-Couette flow, but the method can be applied to many other complex systems in a similar way.