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.
KeywordsDiffusion of InnovationBass’ ModelInteractive Multi-Agent SystemsLocal InteractionsImitation ProcessesStochastic DynamicsAlternating Renewal ProcessesMean-Field DynamicsDiscrete Velocity Collisions ModelsNonlinear Field EquationsExact Transient Evolutions
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