A Consumer Behavior Model With Advertising And Word-of-mouth Effects

It is well-known that people's consumption behavior is influenced by advertising and word-of-mouth effects.Considering this,we propose a mathematical model to interpret the consumer behavior under the advertising and word-of-mouth effects,which is divided into continuous and discrete types for dynamic behavior analysis.It is found that the continuous model undergoes fold bifurcation,Hopf bifurcation,and degenerate fold-Hopf bifurcation;the discrete model undergoes flip bifurcation and Neimark-Sacker bifurcation.Moreover,bifurcation diagrams are given by using MATLAB to illustrate the model behaviors.Based on the theory of Hopf bifurcation or Flip bifurcation,it shows that under certain conditions,the system has supercritical Hopf bifurcation or Flip bifurcation.This means that the advertising impacts periodically on consumer behavior,and a short-term reduction will not affect the public's recognition of the brand,which can better guide advertising investment.