In the article, a model of diffusion of a product with three classes of populations viz. non-adopters from low-income group N1(t), non-adopters from high-income group N2(t) and adopters of the innovation A(t) is proposed to examine the qualitative behavior of an innovation in a region. It is noticed in the model that the increase in adopter’s population is completely affected by the external (advertisements) as well as internal influences (word of mouth communications). Bifurcation in an innovation diffusion model is a phenomenon in which the model possesses stable interior equilibrium together with a stable adopter-free equilibrium. This model established two equilibriums, viz., the adopter-free steady state and an interior steady state. Dynamical behavior and the basic influence number of the proposed system are studied. The presence and local stability of the adopter-free and interior steady state are examined in terms of the effective Basic Influence Number (BIN) (R¬A). It is investigated that the adopter free point is locally stable if R¬A < 1. In this work, the author investigates the possibility of bifurcation in an innovation diffusion model. By considering τ (evaluation time period) as a control parameter, the system has been studied by classical theory of stability and Hopf-bifurcation analysis. The author has been able to investigate that the obtained critical value of parameter τ is responsible for the occurrence of periodic solutions due to Hopf bifurcation. The author believes that the presented research work in this chapter provides an insight of the dynamics of a diffusion model and possible causes of bifurcation in the same. Exhaustive numerical techniques have been applied in the justification of analytical results.