Study on the Stability and Entropy Complexity of an Energy-Saving and Emission-Reduction Model with Two Delays
In this paper, we build a model of energy-savings and emission-reductions with two delays. In this model, it is assumed that the interaction between energy-savings and emission-reduction and that between carbon emissions and economic growth are delayed. We examine the local stability and the existen...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-10-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/18/10/371 |
| _version_ | 1811308288659161088 |
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| author | Jing Wang Yuling Wang |
| author_facet | Jing Wang Yuling Wang |
| author_sort | Jing Wang |
| collection | DOAJ |
| description | In this paper, we build a model of energy-savings and emission-reductions with two delays. In this model, it is assumed that the interaction between energy-savings and emission-reduction and that between carbon emissions and economic growth are delayed. We examine the local stability and the existence of a Hopf bifurcation at the equilibrium point of the system. By employing System Complexity Theory, we also analyze the impact of delays and the feedback control on stability and entropy of the system are analyzed from two aspects: single delay and double delays. In numerical simulation section, we test the theoretical analysis by using means bifurcation diagram, the largest Lyapunov exponent diagrams, attractor, time-domain plot, Poincare section plot, power spectrum, entropy diagram, 3-D surface chart and 4-D graph, the simulation results demonstrating that the inappropriate changes of delays and the feedback control will result in instability and fluctuation of carbon emissions. Finally, the bifurcation control is achieved by using the method of variable feedback control. Hence, we conclude that the greater the value of the control parameter, the better the effect of the bifurcation control. The results will provide for the development of energy-saving and emission-reduction policies. |
| first_indexed | 2024-04-13T09:20:31Z |
| format | Article |
| id | doaj.art-e6a6b7c1185741caa90514a21da6a60c |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T09:20:31Z |
| publishDate | 2016-10-01 |
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| series | Entropy |
| spelling | doaj.art-e6a6b7c1185741caa90514a21da6a60c2022-12-22T02:52:38ZengMDPI AGEntropy1099-43002016-10-01181037110.3390/e18100371e18100371Study on the Stability and Entropy Complexity of an Energy-Saving and Emission-Reduction Model with Two DelaysJing Wang0Yuling Wang1Department of Mathematics and Physics, Bengbu University, Bengbu 233030, ChinaSchool of Economics, South-Central University for Nationalities, Wuhan 430074, ChinaIn this paper, we build a model of energy-savings and emission-reductions with two delays. In this model, it is assumed that the interaction between energy-savings and emission-reduction and that between carbon emissions and economic growth are delayed. We examine the local stability and the existence of a Hopf bifurcation at the equilibrium point of the system. By employing System Complexity Theory, we also analyze the impact of delays and the feedback control on stability and entropy of the system are analyzed from two aspects: single delay and double delays. In numerical simulation section, we test the theoretical analysis by using means bifurcation diagram, the largest Lyapunov exponent diagrams, attractor, time-domain plot, Poincare section plot, power spectrum, entropy diagram, 3-D surface chart and 4-D graph, the simulation results demonstrating that the inappropriate changes of delays and the feedback control will result in instability and fluctuation of carbon emissions. Finally, the bifurcation control is achieved by using the method of variable feedback control. Hence, we conclude that the greater the value of the control parameter, the better the effect of the bifurcation control. The results will provide for the development of energy-saving and emission-reduction policies.http://www.mdpi.com/1099-4300/18/10/371energy-savingsemission-reductionentropystabilitytwo delaysHopf bifurcation |
| spellingShingle | Jing Wang Yuling Wang Study on the Stability and Entropy Complexity of an Energy-Saving and Emission-Reduction Model with Two Delays Entropy energy-savings emission-reduction entropy stability two delays Hopf bifurcation |
| title | Study on the Stability and Entropy Complexity of an Energy-Saving and Emission-Reduction Model with Two Delays |
| title_full | Study on the Stability and Entropy Complexity of an Energy-Saving and Emission-Reduction Model with Two Delays |
| title_fullStr | Study on the Stability and Entropy Complexity of an Energy-Saving and Emission-Reduction Model with Two Delays |
| title_full_unstemmed | Study on the Stability and Entropy Complexity of an Energy-Saving and Emission-Reduction Model with Two Delays |
| title_short | Study on the Stability and Entropy Complexity of an Energy-Saving and Emission-Reduction Model with Two Delays |
| title_sort | study on the stability and entropy complexity of an energy saving and emission reduction model with two delays |
| topic | energy-savings emission-reduction entropy stability two delays Hopf bifurcation |
| url | http://www.mdpi.com/1099-4300/18/10/371 |
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