Bifurcation behaviour of a nonlinear innovation diffusion model with external influences

A nonlinear form of Bass model for innovation diffusion consisting of a system of two variables viz. for adopters and nonadopters population is proposed to lay stress on the evaluation period. The local stability of a positive equilibrium and the existence of Hopf bifurcation are demonstrated by analysing the associated characteristic equation. The critical value of evaluation period is determined beyond which small amplitude oscillations of the adopter and nonadopters population occur, and this critical value goes on decreasing with the increase in carrying capacity of the non-adopters population. The direction and the stability of bifurcating periodic solutions is determined by using the normal form theory and centre manifold theorem. It is observed that the cumulative density of external influences has a significant role in developing the maturity stage (final adoption stage) in the system. Numerical computations are executed to confirm the correctness of theoretical investigations.