title: Emergent user behavior on Twitter modelled by a stochastic differential equation.
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.
authors.affiliation: Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark.
authors.forename: Anders
authors.initials: A
authors.lastname: Mollgaard
authors.affiliation: Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark.
authors.forename: Joachim
authors.initials: J
authors.lastname: Mathiesen
mesh_terms: D000465:Algorithms; D006801:Humans; D008962:Models, Theoretical; D012815:Signal Processing, Computer-Assisted; D061108:Social Media; D013223:Statistics as Topic; D013269:Stochastic Processes