Minor extensions of the logistic equation for growth curves of word counts on online media: parametric observation of diversity of growth in society

Abstract

To understand the growth phenomena in collective human systems, we analyzed monthly word count time series of new vocabularies 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 non-trivial growth curve that starts with an exponential function and asymptotically approaches a power function without a steady state. We also observed a connection between the functional form of growth and the peak-out behavior. 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.