  User dynamics in online social networks have a significant impact on not only
the online community but also real-world activities. As examples, we can
mention explosive user dynamics triggered by social polarization, echo chamber
phenomena, fake news, etc. Explosive user dynamics are frequently called online
flaming. The wave equation-based model for online social networks (called the
oscillation model) is a theoretical model proposed to describe user dynamics in
online social networks. This model can be used to understand the relationship
between explosive user dynamics and the structure of social networks. However,
since the oscillation model was introduced as a purely theoretical model of
social networks, it is necessary to confirm whether the model describes real
phenomena correctly or not. In this paper, we first show a prediction from the
oscillation model; the low-frequency oscillation mode of user dynamics will be
dominant when the structure of online social networks changes so that user
activity is activated. To verify the predictions with actual data, we show
spectral analyses of both the log data of posts on an electronic bulletin board
site and the frequency data of word search from Google Trends. The results
support the predictions from the theoretical model.
