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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.
