A Class of Automata Networks for Difiusion of Innovations Driven by Riccati Equations Automata Networks for Difiusion of Innovations

Innovation difiusion processes are generally described at aggre- gate level with models like the Bass model (1969) and the Generalized Bass Model (1994). However, the recognized importance of communication channels between agents has recently suggested the use of agent-based models, like Cellu- lar Automata. We argue that an adoption process is nested in a communication network that evolves dynamically and implicitly generates a non{constant po- tential market. Using Cellular Automata we propose a two{phase model of an innovation difiusion process. First we describe the Communication Net- work necessary for the awareness of an innovation. Then, we model a nested process representing the proper adoption dynamics. Through a \Mean Field Approximation" we propose a continuous representation of the discrete time equations derived by our Automata Network. This constitutes a special non autonomous Riccati equation, not yet described in well{known international catalogues. The main results refer to the closed form solution of this equation and to the corresponding statistical analysis for identiflcation and inference. We discuss an application in the fleld of bank services.