Taking account of the time-delayed phenomenon in diffusion of new products, we propose the time-delayed Verhulst model and then establish a grey time-delayed Verhulst model using the method of grey differential equations. The related parameter packets of this novel model are obtained under the rule of ordinary least squares (OLS). The results show that the traditional grey Verhulst model is a special example of grey time-delayed Verhulst model which can reflect the time-delayed information effectively. A practical example of market diffusion shows that the modeling accuracy is remarkably improved by using the grey time-delayed Verhulst model presented in this paper.
"Forecasting New Product Diffusion Using Grey Time-Delayed Verhulst Model." J. Appl. Math. 2013 1 - 6, 2013. https://doi.org/10.1155/2013/625028