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.
|Titolo:||Mathematical models of innovation diffusion with stage structure|
|Data di pubblicazione:||2006|
|Citazione:||Mathematical models of innovation diffusion with stage structure / WANG. W; FERGOLA. P; LOMBARDO S; MULONE G. - In: APPLIED MATHEMATICAL MODELLING. - ISSN 0307-904X. - 30:1(2006), pp. 129-146.|
|Appare nelle tipologie:||1.1 Articolo in rivista|