Mathematical Model for Hit Phenomena

TL;DR

This paper introduces a nonlinear dynamical model for hit phenomena in entertainment, using coupled differential equations to describe purchase intentions and communication effects, validated by recent movie revenue data.

Contribution

It presents a novel mathematical framework modeling hit phenomena with nonlinear differential equations incorporating rumor decay and social interactions.

Findings

Model accurately predicts movie revenues

Includes decay time of rumors as a key factor

Matches empirical data from 25 recent movies

Abstract

The mathematical model for hit phenomena in entertainments is presented as a nonlinear, dynamical 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.