ANALYSIS OF DIFFUSION BY DIFFERENTIAL EQUATION MODELS

Abstract

In this paper representative differential equation models for diffusion process are compared. These models are(1)simple logistic curve, (2)harmonic logistic curve, (3)exponential logistic curve, (4)modified exponential curve, (5)Gompertz curve, (6)Bass's model. Logistic-type models((1), (2), (3))are based on the assumption of the effects of the interactions among members in a group.On the other hand, modified exponential curve model is based on the assumption of the effects of the outside information source. Bass's model synthesizes these two components of diffusion process. The six models are applied to data on consumer durables, music records, and information diffusions. The results show that Bass's model yields the better predictions for most of actual data than any other model.