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.

翻译：为理解全国性在线社交媒体中新词汇的增长现象，我们分析了2007年至2019年间约10亿篇日语博客文章中提取的月度词汇时间序列。具体而言，我们首先通过向原始逻辑方程添加一个参数引入扩展逻辑方程，并证明该模型能够一致地再现实际增长曲线的各种模式，如逻辑函数、线性增长和有限时间发散。其次，通过分析模型参数，我们发现典型的增长模式不仅是常出现在各类复杂系统中的逻辑函数，还包括一种非平凡的增长率曲线——始于指数函数，渐近趋于无稳态的幂函数。此外，我们观察到增长函数形式与峰值出现之间的关联。最后，我们证明该模型及其统计特性同样适用于谷歌趋势数据（英语、法语、西班牙语和日语），即全国范围内搜索查询热度的时序数据。