TITLE:
Spatio-Temporal Patterns for a Generalized Innovation Diffusion Model
AUTHORS:
Fariba Hashemi, Max-Olivier Hongler, Olivier Gallay
KEYWORDS:
Diffusion of Innovation; Bass’ Model; Interactive Multi-Agent Systems; Local Interactions; Imitation Processes; Stochastic Dynamics; Alternating Renewal Processes; Mean-Field Dynamics; Discrete Velocity Collisions Models; Nonlinear Field Equations; Exact Transient Evolutions
JOURNAL NAME:
Theoretical Economics Letters,
Vol.2 No.1,
February
23,
2012
ABSTRACT: We construct a model of innovation diffusion that incorporates a spatial component into a classical imitation-innovation dynamics first introduced by F. Bass. Relevant for situations where the imitation process explicitly depends on the spatial proximity between agents, the resulting nonlinear field dynamics is exactly solvable. As expected for nonlinear collective dynamics, the imitation mechanism generates spatio-temporal patterns, possessing here the remarkable feature that they can be explicitly and analytically discussed. The simplicity of the model, its intimate connection with the original Bass’ modeling framework and the exact transient solutions offer a rather unique theoretical stylized frame-work to describe how innovation jointly develops in space and time.