A special case of diffusion in which the probability of a population member adopting an innovation is proportional to the number of current adopters within the population.  It is a mathematical representation of “keeping up with the Joneses.”  If the number of adopters is Yt and a is the saturation level, then the equation

describes the growth of the number of adopters of the innovation over time (b and c are constants controlling the rate of growth). For a discussion of the logistic and related diffusion curves for forecasting, see Meade and Islam (2001).