ABSTRACT
The chapter deals with a non-adopter population from the low-income group N1(t), non-adopters from the high-income group N2(t) and adopters of the innovation A(t) in order to investigate the diffusion of an innovation (product) in a region. The increase in adopter’s population is affected by both external (advertisements) and internal factors (word-of-mouth communications). The role of time delay (evaluation period) in deciding the adoption of an innovation has been observed. This model established two equilibriums, viz., the adopter-free steady state and an interior steady state. The dynamical behaviour and the basic influence number of the proposed system are studied. The stability of the adopter-free and interior steady states are examined in terms of the effective Basic Influence Number (BIN) (RA). It is established that the adopter free point is locally stable if RA < 1. By considering τ (evaluation time period) as a control parameter, the system has been studied by using the classical theory of stability and Hopf-bifurcation analysis. The author has been able to obtain the threshold value of parameter τ responsible for the periodic solutions due to Hopf bifurcation. The author believes that the presented work provides an insight into the dynamics of a diffusion model and possible causes of bifurcation.
