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Entropy 2017, 19(1), 22; doi:10.3390/e19010022

Research Entropy Complexity about the Nonlinear Dynamic Delay Game Model

1,* and 1,*
College of Management Economic, Tianjin University, Tianjin 300072, China
School of Economics, Beijing Wuzi University, Beijing 101149, China
Authors to whom correspondence should be addressed.
Academic Editors: António M. Lopes and J. A. Tenreiro Machado
Received: 9 November 2016 / Revised: 15 December 2016 / Accepted: 22 December 2016 / Published: 9 January 2017
(This article belongs to the Special Issue Complex Systems and Fractional Dynamics)
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Based on the research of domestic and foreign scholars, this paper has improved and established a double oligopoly market model of renewable energy, and analyzed the complex dynamic characteristics of a system based on entropy theory and chaos theory, such as equilibrium point, stability, Hopf bifurcation conditions, etc. This paper also studied and simulated the effects of the natural growth rate of energy and the single delay decision on the renewable energy system by minimizing the entropy of the system and reducing the system instability to a minimum, so that the degree of disorder within the system was reduced. The results show that with the increase of the natural growth rate of energy, the stability of the system is not affected, but the market demand of the oligopoly 1 is gradually reducing and the market demand of the oligopoly 2 is gradually increasing. At the same time, a single oligopoly making the time delay decision will affect the stability of the two oligopolies. With the increase of delay, the time required to reach the stable state will grow, and the system will eventually enter the Hopf bifurcation, thus the system will have its entropy increased and fall into an unstable state. Therefore, in the actual market of renewable energy, oligopolies should pay attention to the natural growth rate of energy and time delay, ensuring the stability of the game process and the orderliness of the system. View Full-Text
Keywords: renewable energy; natural growth rate; oligopoly game; time delay; Hopf bifurcation; entropy complexity renewable energy; natural growth rate; oligopoly game; time delay; Hopf bifurcation; entropy complexity

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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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Zhan, X.; Ma, J.; Ren, W. Research Entropy Complexity about the Nonlinear Dynamic Delay Game Model. Entropy 2017, 19, 22.

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