Technology diffusion model with distributed delay

摘要

In this paper, we analyze a technology diffusion model with distributed time delay. In the process of adoption a technology, a firm takes into account the advertising effectiveness, government policy and production costs. The average time for making the final decision is introduced. The mathematical model is described by a system with three nonlinear differential equations with distributed delays. When the distributions are Dirac, the cases with one delay and two different delays are considered and we set the conditions for the existence of a Hopf bifurcation. The last part of the paper includes numerical simulations and conclusions.