Bifurcation analysis of a nonlinear diffusion model: Effect of evaluation period for the diffusion of a technology

A nonlinear modified form of Bass model involving the interactions of non-adopter and adopter populations has been proposed to describe the process of diffusion of a new technology in the presence of evaluation period (time delay). The basic aim is to model the diffusion of those technologies which require higher investments, and which require government subsidies for promotions in the various markets. We use government incentives and the costs in the form of external factors, as well as the internal word of mouth that considerably influence the non-adopters decisions. A qualitative analysis has been performed to determine the stability of the various equilibria. The Hopf bifurcation occurs near the positive equilibrium when the time delay passes some critical values. By applying the normal form theory and the center manifold reduction for functional differential equations, explicit formulae presenting stability properties of bifurcating periodic solutions have been computed. Moreover, the intra-specific competition has played an important role in establishing the maturity stage in the innovation diffusion model. Numerical analysis has been carried out to justify the correctness of our analytical findings.