Long-term memory on popularity dynamics: insights from the Billboard Hot 100 chart

This study delves into the dynamics of popularity as a crucial aspect of population dynamics, drawing from ecology and social science literature. The focus is on constructing an accurate model for understanding the spread of novelty, memes, and influences within human society, particularly through online platforms such as YouTube, Twitter, and Amazon. Traditional models, based on logistic and similar nonlinear differential equations, have shown limitations in long-term prediction accuracy, partially due to unexplained deviations. Recent research suggests the significance of long-term memory effects on popularity, characterized by a power-law response function, a phenomenon particularly evident in the realm of online mass media. Our research analyzes the Billboard Hot 100 chart, a comprehensive dataset of music popularity spanning several decades, to examine these dynamics. By integrating logistic growth with a power-law decaying long-term memory model, we demonstrate that the trajectory of popularity rankings is predominantly influenced by initial popularity levels and the strength of memory effects. Our findings reveal the pivotal role of long-term memory and the extent of initial popularity in shaping popularity dynamics over time. The study underscores the impact of mass media evolution and the differential effects of spreading mechanisms and accumulated popularity on these dynamics, particularly when long-term memory is a factor. This work contributes to a deeper understanding of the mechanisms driving popularity and its long-term trends in the digital age.