Year: 2019
Author: Peidi Nie, M. A. Abd-Rabo, Yutong Sun, Jingli Ren
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 4 : pp. 461–489
Abstract
It is widely-held belief that people'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's recognition of the brand, which can guide precision advertising investment.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2019.461
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 4 : pp. 461–489
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: The consumption behaviour model Hopf bifurcation fold bifurcation Flip bifurcation Neimark-Sacker bifurcation.