Fariba Hashemi, Max-Olivier Hongler, Olivier Gallay
IBM Zurich Research Laboratory, Mathematical and Computational Sciences Department, Rueschlikon, Switzerland.
Swiss Federal Institute of Technology, College of Management of Technology, Lausanne, Switzerland.
Swiss Federal Institute of Technology, School of Engineering, Laboratory of Micro engineeringfor Manufacturing, Lausanne, Switzerland.
DOI: 10.4236/tel.2012.21001   PDF    HTML     5,875 Downloads   10,811 Views   Citations

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.

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

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Conflicts of Interest

The authors declare no conflicts of interest.

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