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| A Consumption Behavior Model with Advertising And Word-of-Mouth Effect |
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| KeyWord:The consumption behaviour model Hopf bifurcation fold bifurcation Flip bifurcation Neimark-Sacker bifurcation |
| Author Name | Affiliation | | Peidi Nie | School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China | | M. A. Abd-Rabo | School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China | | Yutong Sun | School of Business, Macau University of Science and Technology, Avenida Wai Long, Taipa, Macau, China | | Jingli Ren | School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
Henan Academy of Big Date, Zhengzhou University, Zhengzhou 4500051, China |
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| 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 lead 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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