Mathematical models of innovation diffusion with stage structure

Abstract

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.

A multi‐stage ‘infection’ model of stock investors' reaction to new product announcement signal

“…Previously, scholars tend to look upon the relationship between NPA and stock market response statically, which can be perceived from their attention on the static results in the way of statistical analysis or basic empirical research. Synthesizing previous research [21][22][23][24] and considering the behavioral characteristics of stock investors, we conclude that the process that NPA signal diffuses in stock market consists of three stages: awareness, evaluation, and investment. The multi-stage process provides a channel to observe the dynamic procedure of stock investor behavior and lucubrate the internal influence mechanism of this issue.…”

Forecasting innovation diffusion of products using trend-weighted fuzzy time-series model

“…where p is the coefficient of innovation (or the coefficient of external influence), q is the coefficient of imitation (or the coefficient of internal influence), f(t) is the probability density function of adoption at time t, and F(t) is the cumulated density function of adoption at time t. From the Bass model, it is easily understandable that the effect of external influence and internal influence is immediate and the maximal market potential will be eventually reached (Wang, Fergola, Lombardo, & Mulone, 2006). For simplicity, the Bass model describes the diffusion process by a first-order differential equation as follows (Osaki, Gemba, & Fumio, 2001;Wang et al, 2006):…”

“…For simplicity, the Bass model describes the diffusion process by a first-order differential equation as follows (Osaki, Gemba, & Fumio, 2001;Wang et al, 2006):…”

Adoption of Administrative Innovation Within Organization — An Empirical Study of TQM Metamorphosis

“…The ability to adopt the innovation and the innovation adoption process have been widely studied issues in the innovation literature [Kim and Kim (2004); Wang et al (2006); Yeon et al (2006)], and there is already quite a comprehensive amount of research done about the diffusion and adoption models [Kline (1985); Baskerville and Pries-Heje (2001); Kamrad et al (2005)]. …”