Reinforcement-driven spread of innovations and fads

We propose kinetic models for the spread of permanent innovations and fads by the mechanism of social reinforcement. Each individual can be one of M+1 states of awareness 0,1,2,...,M, with state M corresponding to an innovation. An individual with awareness k<M increases to k+1 by with an adopter. Starting with a single adopter, the time for an unaware population of size N to adopt a permanent innovation grows as(N) for M=1, and as N1-1/M for M>1. The fraction of the population that clueless about a transient fad after it has come and gone changes as a function of the fad abandonment rate lambda for M>1. The dies out completely in a time that varies non-monotonically with lambda.