Universal features of correlated bursty behaviour

TL;DR

This paper reveals that the distribution of events within bursty periods universally follows a power-law across various systems, and introduces a simple model to explain the observed temporal correlations based on memory effects.

Contribution

It demonstrates that the distribution of events in bursty intervals is a universal indicator of temporal dependencies and proposes a phenomenological model capturing these effects.

Findings

Power-law distribution of events in bursty periods across systems

Correlations explained by memory effects in a simple model

Universal features observed in human, neural, and seismic data

Abstract

Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty behavior has been characterized by a fat-tailed inter-event time distribution, while temporal correlations were measured by the autocorrelation function. However, these characteristic functions are not capable to fully characterize temporally correlated heterogenous behavior. Here we show that the distribution of the number of events in a bursty period serves as a good indicator of the dependencies, leading to the universal observation of power-law distribution in a broad class of phenomena. We find that the correlations in these quite different systems can be commonly interpreted by memory effects and described by a simple phenomenological model, which displays temporal behavior qualitatively similar to that in real systems.