Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product
In this paper, a mixed duopoly dynamic model with bounded rationality is built, where a public-private joint venture and a private enterprise produce homogeneous products and compete in the same market. The purpose of this research is to study the stability and the multistability of the established...
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Online Access: | http://dx.doi.org/10.1155/2020/4580415 |
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doaj-c4def9e0b57f410fa47eb50f40bf0a3c2020-11-25T03:52:04ZengHindawi-WileyComplexity1076-27871099-05262020-01-01202010.1155/2020/45804154580415Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous ProductWei Zhou0Na Zhao1Tong Chu2Ying-Xiang Chang3School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaSchool of Law, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang 310018, ChinaSchool of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaIn this paper, a mixed duopoly dynamic model with bounded rationality is built, where a public-private joint venture and a private enterprise produce homogeneous products and compete in the same market. The purpose of this research is to study the stability and the multistability of the established model. The local stability of all the equilibrium points is discussed by using Jury condition, and the stability region of the Nash equilibrium point has been given. A special fractal structure called “hub of periodicity” has been found in the two-parameter space by numerical simulation. In addition, the phenomena of multistability (also called coexistence of multiple attractors) are also studied using basins of attraction and 1-D bifurcation diagrams with adiabatic initial conditions. We find that there are two different coexistences of multiple attractors. And, the fractal structure of the attracting basin is also analyzed, and the formation mechanisms of “holes” and “contact” bifurcation have been revealed. At last, the long-term profits of the enterprises are studied. We find that some enterprises can even make more profits under a chaotic circumstance.http://dx.doi.org/10.1155/2020/4580415 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Wei Zhou Na Zhao Tong Chu Ying-Xiang Chang |
spellingShingle |
Wei Zhou Na Zhao Tong Chu Ying-Xiang Chang Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product Complexity |
author_facet |
Wei Zhou Na Zhao Tong Chu Ying-Xiang Chang |
author_sort |
Wei Zhou |
title |
Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product |
title_short |
Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product |
title_full |
Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product |
title_fullStr |
Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product |
title_full_unstemmed |
Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product |
title_sort |
stability and multistability of a bounded rational mixed duopoly model with homogeneous product |
publisher |
Hindawi-Wiley |
series |
Complexity |
issn |
1076-2787 1099-0526 |
publishDate |
2020-01-01 |
description |
In this paper, a mixed duopoly dynamic model with bounded rationality is built, where a public-private joint venture and a private enterprise produce homogeneous products and compete in the same market. The purpose of this research is to study the stability and the multistability of the established model. The local stability of all the equilibrium points is discussed by using Jury condition, and the stability region of the Nash equilibrium point has been given. A special fractal structure called “hub of periodicity” has been found in the two-parameter space by numerical simulation. In addition, the phenomena of multistability (also called coexistence of multiple attractors) are also studied using basins of attraction and 1-D bifurcation diagrams with adiabatic initial conditions. We find that there are two different coexistences of multiple attractors. And, the fractal structure of the attracting basin is also analyzed, and the formation mechanisms of “holes” and “contact” bifurcation have been revealed. At last, the long-term profits of the enterprises are studied. We find that some enterprises can even make more profits under a chaotic circumstance. |
url |
http://dx.doi.org/10.1155/2020/4580415 |
work_keys_str_mv |
AT weizhou stabilityandmultistabilityofaboundedrationalmixedduopolymodelwithhomogeneousproduct AT nazhao stabilityandmultistabilityofaboundedrationalmixedduopolymodelwithhomogeneousproduct AT tongchu stabilityandmultistabilityofaboundedrationalmixedduopolymodelwithhomogeneousproduct AT yingxiangchang stabilityandmultistabilityofaboundedrationalmixedduopolymodelwithhomogeneousproduct |
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1715099993646301184 |