Akira Ishii, Sanae Umemura, Takefumi Hayashi, Naoya Matsuda ∗ 

# Mathematical Model of Hit Phenomena 

Department of Applied Mathematics and Physics, 

Tottori University, Koyama, Tottori 680-8552, Japan 

Takeshi Nakagawa 

Dentsu Inc., 1 -8-1, Higashi-shimbashi, Minato-ku, Tokyo 105-7001, Japan 

Digital Hollywood University, DH2001 Bldg. 2-3 Surugadai, 

Hisashi Arakaki, Narihiko Yoshida 

Kanda, Chiyoda-ku, Tokyo, 101-0062 

## Abstract 

The mathematical model for hit phenomena in entertainments is presented as a nonlinear, dy- namical and non-equilibrium phenomena. The purchase intention for each person is introduced and direct and indirect communications are expressed as two-body and three-body interaction in our model. The mathematical model is expressed as coupled nonlinear differential equations. The important factor in the model is the decay time of rumor for the hit. The calculated results agree very well with revenues of recent 25 movies. 

Keywords: mathematical model, blog, movie, hit, advertisement 

