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Entropy and Stability Analysis of Delayed Energy Supply–Demand Model

Department of Mathematics and Physics, Bengbu University, Bengbu 233030, China
School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China
School of Economics, South-Central University for Nationalities, Wuhan 430074, China
Authors to whom correspondence should be addressed.
Academic Editor: J. A. Tenreiro Machado
Entropy 2016, 18(12), 434;
Received: 21 October 2016 / Revised: 27 November 2016 / Accepted: 29 November 2016 / Published: 3 December 2016
(This article belongs to the Section Complexity)
In this paper, a four-dimensional model of energy supply–demand with two-delay is built. The interactions among energy demand of east China, energy supply of west China and the utilization of renewable energy in east China are delayed in this model. We discuss stability of the system affected by parameters and the existence of Hopf bifurcation at the equilibrium point from two aspects: single delay and two-delay. The stability and complexity of the system are demonstrated through bifurcation diagram, Poincare section plot, entropy diagram, etc. in numerical simulation. The simulation results show that the parameters beyond the stable region will cause the system to be unstable and increase the complexity of the system. At this point, because of energy supply–demand system fluctuations, it is difficult to formulate energy policies. Finally, the bifurcation control is realized successfully by the method of delayed feedback control. The results of bifurcation control simulation indicate that the system can return to stable state by adjusting the control parameter. In addition, we find that the bigger the value of the control parameter, the better the effect of the bifurcation control. The results of this paper can provide help for maintaining the stability of the system, which will be conducive to energy scheduling. View Full-Text
Keywords: energy supply–demand; Hopf bifurcation; entropy; stability; two-delay energy supply–demand; Hopf bifurcation; entropy; stability; two-delay
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Wang, J.; Si, F.; Wang, Y.; Duan, S. Entropy and Stability Analysis of Delayed Energy Supply–Demand Model. Entropy 2016, 18, 434.

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