Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imita...

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Bibliographic Details
Published in:Applied mathematical modelling 2006, Vol.30 (1), p.129-146
Main Authors: Wang, Wendi, Fergola, P., Lombardo, S., Mulone, G.
Format: Article
Language:English
Subjects:
Applied sciences
Bistable equilibria
Decision theory. Utility theory
Exact sciences and technology
Innovation diffusion
Operational research and scientific management
Operational research. Management science
Stability switches
Stage structure
Time delay
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Summary:Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.
ISSN:0307-904X
DOI:10.1016/j.apm.2005.03.011