A Consumption Behavior Model with Advertising and Word-of-Mouth Effect (Journal of Nonlinear Modeling and Analysis, 2024)
It is widely-held belief that people's consumption behavior is partlydetermined by advertising and word-of-mouth effect especially in monopolistic competitive market. Owing to this, we propose a mathematical model tointerpret consumer behavior under the advertising and word-of-mouth effects,which is divided into continuous and discrete types for dynamic behavior analysis. Our research indicates the continuous model undergoes fold bifurcation,Hopf bifurcation, and degenerate fold-Hopf bifurcation; the discrete model undergoes flip bifurcation and Neimark-Sacker bifurcation. Moreover, bifurcationdiagrams are given by using MATLAB to illustrate the model. Based on thetheory of Hopf bifurcation or Flip bifurcation, the system undergoes supercritical Hopf bifurcation or Flip bifurcation under certain conditions. This leads toboth advertising impacts periodically on consumer behavior, and a short-termreduction cause no effect the public's recognition of the brand, which can guideprecision advertising investment.
Keywords: The consumption behaviour model; Hopf bifurcation; fold bifurcation; Flip bifurcation; Neimark-Sacker bifurcation.