An economic group model for innovation diffusion of new product with delay of adoption for low income group

In this paper, an economic group delay model is established. Dynamical behavior and Basic influence number of the proposed system are studied. Asymptotic stability analysis is carried out for the steady-states. The critical value of the delay \tau is determined. It is observed that for the interior steady-state remains stable if the adoption delay for the low-income group is less than the threshold value, i.e., \tau<\tau_{۰}^+. If \tau crosses its threshold, system perceives oscillating behavior, and Hopf bifurcation occurs. Moreover, sensitivity analysis is performed for the system parameter used in the interior steady-state. Finally, numerical simulations are conducted to support our analytical findings.

Keywords:

Boundedness , positivity , delay , Hopf bifurcation , sensitivity analysis