Abstract: We established a multi-stage dynamic model to reflect the  characteristics of product  word-of-mouth communication based on  the laws of product word-of-mouth communication. Firstly, using qualitative analysis and stability theory, we analyzed the existence and stability of the model’s equilibrium points, and gave the conditions for the existence of backward bifurcation. Secondly, the Lyapunov function was used to demonstrate the global asymptotic stability of  the model’s information-free equilibrium point and the positive equilibrium point when a=0.  Finally, we  found  that the model  underwent saddle-node bifurcation, Hopf bifurcation, B-T bifurcation, and degenerate Hopf bifurcation through numerical simulation. The results show  that the coupling effect between product buyers and active disseminators of product word-of-mouth has a significant effect on the dynamic process of word-of-mouth communication.

Key words: word-of-mouth communication, basic reproduction number, backward bifurcation, stability