  Popularity describes the dynamics of mass attention, and is a part of a
broader class of population dynamics in ecology and social science literature.
Studying accurate model of popularity is important for quantifying spreading of
novelty, memes, and influences in human society. Although logistic equation and
similar class of nonlinear differential equation formulates traditional
population dynamics well, part of the deviation in long-term prediction is
stated, yet fully understood. Recently, several studies hinted a long-term
memory effect on popularity whose response function follows a power-law,
especially that appears on online mass media such as YouTube, Twitter, or
Amazon book sales. Here, we investigate the ranking of most popular music,
\textit{the Billboard Hot 100 chart}, which is one of the largest popularity
dataset spanning several decades. Using a popularity model that comprises
logistic growth and a power-law decaying long-term memory, we showed that rank
history is mainly characterized by initial popularity and memory strength. With
this framework, we investigated temporal development of long-term memory on the
whole popularity dynamics. As a result, abrupt emergence of long-term memory
and broad initial popularity is illustrated, which was not clearly detected by
time-independent measures. We emphasize not only development of the mass media,
but also the difference of spreading and accumulated popularity affect dynamics
significantly when the popularity has long-term memory.
