Increase of Low-Frequency Modes of User Dynamics in Online Social Networks During Overheating of Discussions

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.