A time delay model for a new technology

In this paper we propose a mathematical model with time delay to describe the process of the diffusion for a new technology. This model is suitable for modelling diffusion processes of all those technologies, such as technologies used for producing renewable energy, that require great initial investments and public subsidies. We consider external factors, such as the government policy and the production costs, that influence the decision making process for new technology adoption. We also consider the internal influence from those who already are adopters. The time delay represents the evaluation stage at which the potential consumers decide whether to adopt the new technology or not. A delay differential equation describes the process of adoption. A qualitative analysis is carried out in order to study the stability of the equilibrium for certain parameters and to find the final level of adopters.