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Entropy 2016, 18(9), 317; doi:10.3390/e18090317

Entropy Complexity and Stability of a Nonlinear Dynamic Game Model with Two Delays

1
College of Management and Economics, Tianjin University, Tianjin 300072, China
2
School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China
*
Authors to whom correspondence should be addressed.
Academic Editors: J. A. Tenreiro Machado and António M. Lopes
Received: 13 June 2016 / Revised: 17 August 2016 / Accepted: 17 August 2016 / Published: 30 August 2016
(This article belongs to the Special Issue Computational Complexity)
View Full-Text   |   Download PDF [3453 KB, uploaded 30 August 2016]   |  

Abstract

In this paper, a duopoly game model with double delays in hydropower market is established, and the research focus on the influence of time delay parameter on the complexity of the system. Firstly, we established a game model for the enterprises considering both the current and the historical output when making decisions. Secondly, the existence and stability of Hopf bifurcation are analyzed, and the conditions and main conclusions of Hopf bifurcation are given. Thirdly, numerical simulation and analysis are carried out to verify the conclusions of the theoretical analysis. The effect of delay parameter on the stability of the system is simulated by a bifurcation diagram, the Lyapunov exponent, and an entropic diagram; in addition, the stability region of the system is given by a 2D parameter bifurcation diagram and a 3D parameter bifurcation diagram. Finally, the method of delayed feedback control is used to control the chaotic system. The research results can provide a guideline for enterprise decision-making. View Full-Text
Keywords: duopoly game; two delays; bifurcation and chaos; entropy; system stability duopoly game; two delays; bifurcation and chaos; entropy; system stability
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Han, Z.; Ma, J.; Si, F.; Ren, W. Entropy Complexity and Stability of a Nonlinear Dynamic Game Model with Two Delays. Entropy 2016, 18, 317.

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