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Mathematical models of innovation diffusion with stage structure. (English) Zbl 1106.37309
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:
37N40Dynamical systems in optimization and economics
90B50Management decision making, including multiple objectives
91B42Consumer behavior, demand theory