TY - JOUR
T1 - A Consumption Behavior Model with Advertising and Word-of-Mouth Effect
AU - Nie , Peidi
AU - Abd-Rabo , M. A.
AU - Sun , Yutong
AU - Ren , Jingli
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 461
EP - 489
PY - 2021
DA - 2021/04
SN - 1
DO - http://doi.org/10.12150/jnma.2019.461
UR - https://global-sci.org/intro/article_detail/jnma/18835.html
KW - The consumption behaviour model, Hopf bifurcation, fold bifurcation, Flip bifurcation, Neimark-Sacker bifurcation.
AB - <p style="text-align: justify;">It is widely-held belief that people&#39;s consumption behavior is partly
determined by advertising and word-of-mouth effect especially in monopolistic competitive market. Owing to this, we propose a mathematical model to
interpret 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, bifurcation
diagrams are given by using MATLAB to illustrate the model. Based on the
theory of Hopf bifurcation or Flip bifurcation, the system undergoes supercritical Hopf bifurcation or Flip bifurcation under certain conditions. This leads to
both advertising impacts periodically on consumer behavior, and a short-term
reduction cause no effect the public&#39;s recognition of the brand, which can guide
precision advertising investment.</p>