Nested-layer particle swarm optimization (NLPSO) is a powerful method to detect bifurcation parameters in dynamical systems. Although NLPSO requires no carefully set initial system parameters, Lyapunov exponents, or the derivative of objective functions, the method can accurately detect bifurcation parameters. However, NLPSO has a serious problem in that it fails to detect a target bifurcation parameter when various types of bifurcation parameters with various periods coexist within the search parameter space. In this study, we clarify problems in detecting bifurcation parameters using conventional NLPSO and solve them by adding a penalty term and imposing a simple condition on the NLPSO objective functions. Using these extended objective functions, NLPSO accurately detected target bifurcation parameters.

User dynamics in online social networks have a significant impact not only on the online community but also on real-world activities. Therefore, understanding online user dynamics has become a significant issue. 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 dynamics 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.