Excitable human dynamics driven by extrinsic events in massive communities

Significance Online social networks have over the last decade influenced the way people interact. Data from Twitter allow for a detailed study of the activity in online massive communities. By studying the frequency by which international brands appear on Twitter and the trade of financial securities on financial markets, we find a characteristic bursty behavior of the activity levels of Twitter users and market participants. We explain the bursty behavior by a simple model of the large-scale human behavior and quantify the correlations in the activity levels. The statistical similarity of the two social systems is an indication that the complex process underlying individual decision-making might not be very different for Twitter users and participants in financial markets. Using empirical data from a social media site (Twitter) and on trading volumes of financial securities, we analyze the correlated human activity in massive social organizations. The activity, typically excited by real-world events and measured by the occurrence rate of international brand names and trading volumes, is characterized by intermittent fluctuations with bursts of high activity separated by quiescent periods. These fluctuations are broadly distributed with an inverse cubic tail and have long-range temporal correlations with a power spectrum. We describe the activity by a stochastic point process and derive the distribution of activity levels from the corresponding stochastic differential equation. The distribution and the corresponding power spectrum are fully consistent with the empirical observations.