A minor extension of the logistic equation for growth of word counts on online media: Parametric description of diversity of growth phenomena in society

To understand the growing phenomena of new vocabulary on nationwide online social media, we analyzed monthly word count time series extracted from approximately 1 billion Japanese blog articles from 2007 to 2019. In particular, we first introduced the extended logistic equation by adding one parameter to the original equation and showed that the model can consistently reproduce various patterns of actual growth curves, such as the logistic function, linear growth, and finite-time divergence. Second, by analyzing the model parameters, we found that the typical growth pattern is not only a logistic function, which often appears in various complex systems, but also a nontrivial growth curve that starts with an exponential function and asymptotically approaches a power function without a steady state. Furthermore, we observed a connection between the functional form of growth and the peak-out. Finally, we showed that the proposed model and statistical properties are also valid for Google Trends data (English, French, Spanish, and Japanese), which is a time series of the nationwide popularity of search queries.