Cellular automata with network incubation period versus perturbed Riccati equation models in information technology innovation diffusion

Innovation diffusion of network goods determines direct network externalities that exhibit delayed full benefits depressing sales for long periods. We model a multiplicative dynamic potential market driven by a latent heterogeneous individual threshold derived from a basic economic theory which is embedded in a special Cellular Automata representation. The corresponding mean field approximation of its aggregate version is a Riccati equation with a closed form solution that allows a separation between an incubation period and a subsequent take–off due to a sufficient critical mass. Weighted nonlinear least squares methodology is the main inferential technique. An application is analyzed with reference to USA fax machines diffusion.