Dynamic analysis and chaos control of Bertrand triopoly based on differentiated products and heterogeneous expectations
type: Item
instance of: scholarly article
title: Dynamic analysis and chaos control of Bertrand triopoly based on differentiated products and heterogeneous expectations
zbMATH Open document ID: 1459.91095
DOI: 10.1155/2020/2012680
author: Liuwei Zhao
published in: Discrete Dynamics in Nature and Society
publication date: 2020-07-22T00:00:00Z
review text: Summary: Price competition has become a universal commercial phenomenon nowadays. This paper considers a dynamic Bertrand price game model, in which enterprises have heterogeneous expectations. By the stability theory of the dynamic behavior of the Bertrand price game model, the instability of the boundary equilibrium point and the stability condition of the internal equilibrium point are obtained. Furthermore, bifurcation diagram, basin of attraction, and critical curve are introduced to investigate the dynamic behavior of this game. Numerical analysis shows that the change of model parameters in a dynamic system has a significant impact on the stability of the system and can even lead to complex dynamic behaviors in the evolution of the entire economic system. This kind of complex dynamic behavior will cause certain damage to the stability of the whole economic system, causing the market to fall into a chaotic state, which is manifested as a kind of market disorder competition, which is very unfavorable to the stability of the economic system. Therefore, the chaotic behavior of the dynamical system is controlled by time-delay feedback control and the numerical analysis shows that the effective control of the dynamical system can be unstable behavior and the rapid recovery of the market can be stable and orderly.
Mathematics Subject Classification ID: 91B55
zbMATH DE Number: 7224130
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/2012680
OpenAlex ID: W3042050002
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description: scientific article; zbMATH DE number 7224130