## INTRODUCTION 

Hit phenomena in entertainments are very popular dynamical phenomena in economics. In contrast to the usual economic activities, there are no balances of demand and supply in hit phenomena. Thus, for analysis of hit phenomena, we consider it as time-dependent non-equilibrium phenomena. Moreover, especially for movie hits, the marketing share is not important. The significant factors for movie hit are the movie itself is attractive or not. Therefore, we can consider the hit for each movie individually. 

In this study, we consider the hit phenomena of movies with both experimental and theoretical ways. For experimental viewpoint, we observe daily revenue data and daily blog- writing data for many movies. We also obtain the advertisement cost for the movies. For theoretical viewpoint, we present here a mathematical model for hit phenomena as non- equilibrium, nonlinear and dynamical phenomena. Comparing the simulated revenue with the observed revenue for the movies checks the model. The model presented in this paper is based on the previous works.[1],[2] 

## OBSERVATION OF HIT EVIDENCE 

We observe three data of recent 25 popular movies for daily revenue, daily advertisement costs and the entry number of blog writing in Japanese market. The revenue data is obtained from Nikkan Kogyo Tsushinsya in Japan. The advertisement cost data are obtained from Dentsu inc. The blog writing data is collected using the site ”Kizasi”. 

First, as shown in fig.1, we found that the revenues decrease almost exponentially. This evidence is very natural, because the number of audience decrease monotonically due to the effect that person who watched the movie does not watch the same movie again. In fig.1, only the data E shows the sudden decrease. It happens due to the sudden accident of the actress of the movie. From the data, we found that the decay factors for most of all movies in fig.1 seems to be similar. The decay factor of the exponential decay is nearly 0.06 per day. It agrees well with the empirical rule of the Japanese movie market that the number of audience decrease roughly 6 percents. 

This exponential decrease can be explained easily by using a simple mathematical model. First, we define that the number of potential audience to be N$_{0}$ and the number of integrated 

