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Zbl 1106.37309
Wang, Wendi; Fergola, P.; Lombardo, S.; Mulone, G.
Mathematical models of innovation diffusion with stage structure. (English)
[J] Appl. Math. Modelling 30, No. 1, 129-146 (2006). ISSN 0307-904X

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 discussed, too.

MSC 2000:: *37N40 Dynamical systems in optimization and economics
90B50 Multiple-criteria decision making
91B42 Consumer behavior etc.

Keywords: innovation diffusion; stage structure; bistable equilibria; stability switches; time delay

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