Stability And Bifurcation Analysis Of A Nonlinear Innovation Diffusion Model

A modified nonlinear version of the Bass model entailing the non-adopting and adopting population analyzed to understand the diffusing of a new creative technology in a time-delayed differential equation.The main goal is to model the diffusion of innovations requiring higher investment and requiring government contributions for its advancements in different markets and how that factor affects the adoption level of a particular technology when infused into a social system.We analyze the stableness,Hopf bifurcation occurrence and the directional forms of bifurcation of the system considering a free and wider population.When the time delay parameter moves through some critical numbers,Hopf bifurcation occurs near a non-negative equilibrium.The parametric numerical simulation has been performed to get a better understanding.