Diffusion and Growth: The Non-Homogeneous Case

Abstract

Lekvall & Wahlbin (1973) have suggested that the right-hand skew often observed in growth and diffusion curves can be assumed to be the overt outcome of a combined exponential and logistic process. In this article it is argued that the skew in the cumulative distributions can also be accounted for not only by structural heterogeneity in the target population, but also by dynamic heterogeneity when the population changes as the process goes on, or by changing stimulus effects. Two simple models-one modifying the logistic and the other modifying the exponential function-are introduced. They can account not only for right-hand but also for left-hand skew, and have the logistic and exponential functions, respectively, as special cases. Since both of the models can give rise to S-shaped and J-shaped curves, it is argued that the shape of the growth curve in itself provides little information about the underlying process. The models can be combined, after which they yield a Riccati equation. The first model is illustrated by the spread of TV ownership in Norway.