HOPF BIFURCATION ANALYSIS OF DIFFUSIVE BASS MODEL WITH DELAY UNDER "NEGATIVE-WORD-OF-MOUTH"

The original Bass product growth model has been modified in this paper by incorporating a diffusion term and a delay. The imitation parameter beta is assumed to be negative which represents the effect of "negative-word-of-mouth" (NWOM). The occurrence of Hopf bifurcation at the positive equilibrium of the remaining market growth u* was proved as beta passes through a critical value. The analysis of the distribution of eigenvalues led to the following conclusion. The unstable positive equilibrium state at zero diffusion (d = 0) under NWOM becomes stable when d > 0 for a wide range of beta. This observation suggests that when there is a critical NWOM, favorable conditions for the future stable state of u* could be achieved by promoting the product in space (new geographical areas).