Emergent user behavior on Twitter modelled by a stochastic differential equation

TL;DR

This paper models collective user behavior on Twitter using a stochastic differential equation with multiplicative noise, capturing bursty dynamics and 1/f noise observed in tweet rate fluctuations.

Contribution

It introduces a novel stochastic differential equation model that accurately reproduces Twitter user interest dynamics and bursty tweet rate fluctuations.

Findings

Model reproduces bursty tweet dynamics

Captures 1/f noise in tweet rate fluctuations

Supports analysis of collective human behavior

Abstract

Data from the social-media site, Twitter, is used to study the fluctuations in tweet rates of brand names. The tweet rates are the result of a strongly correlated user behavior, which leads to bursty collective dynamics with a characteristic 1/f noise. Here we use the aggregated "user interest" in a brand name to model collective human dynamics by a stochastic differential equation with multiplicative noise. The model is supported by a detailed analysis of the tweet rate fluctuations and it reproduces both the exact bursty dynamics found in the data and the 1/f noise.