| Effects of Hard Limits on Bifurcation, Chaos and Stability |
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| 引用本文： | Rui-qiWang Ji-caiHuang. Effects of Hard Limits on Bifurcation, Chaos and Stability[J]. 应用数学学报(英文版), 2004, 20(3): 441-456. DOI: 10.1007/s10255-004-0183-x |
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| 作者姓名： | Rui-qiWang Ji-caiHuang |
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| 作者单位： | AcademyofMathematicsandSystemsScience,ChineseAcademyofSciences,Beijing,100080,China |
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| 基金项目： | Supported by The National Key Basic Research Fundation (No.G1998020307) |
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| 摘 要： | An SMIB model in the power systems,especially that concering the effects of hard limits onbifurcations,chaos and stability is studied.Parameter conditions for bifurcations and chaos in the absence ofhard limits are compared with those in the presence of hard limits.It has been proved that hard limits can affectsystem stability.We find that (1) hard limits can change unstable equilibrium into stable one;(2) hard limits canchange stability of limit cycles induced by Hopf bifurcation;(3) persistence of hard limits can stabilize divergenttrajectory to a stable equilibrium or limit cycle;(4) Hopf bifurcation occurs before SN bifurcation,so the systemcollapse can be controlled before Hopf bifurcation occurs.We also find that suitable limiting values of hard limitscan enlarge the feasibility region.These results are based on theoretical analysis and numerical simulations,such as condition for SNB and Hopf bifurcation,bifurcation diagram,trajectories,Lyapunov exponent,Floquetmultipliers,dimension of attractor and so on.
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| 关 键 词： | SMIB 分枝 模糊 稳定性 可能性域 微分方程 |
| 收稿时间： | 2003-09-25 |
Effects of Hard Limits on Bifurcation,Chaos and Stability |
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| Rui-qi?WangEmail author,Ji-cai?Huang. Effects of Hard Limits on Bifurcation,Chaos and Stability[J]. Acta Mathematicae Applicatae Sinica, 2004, 20(3): 441-456. DOI: 10.1007/s10255-004-0183-x |
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| Authors: | Rui-qi?Wang author-information" > author-information__contact u-icon-before" > mailto:rqwang@mail.amss.ac.cn" title=" rqwang@mail.amss.ac.cn" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Ji-cai?Huang |
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| Affiliation: | E-mail:rqwang@mail.amss.ac.cn |
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| Abstract: | An SMIB model in the power systems,especially that concering the effects of hard limits onbifurcations,chaos and stability is studied.Parameter conditions for bifurcations and chaos in the absence ofhard limits are compared with those in the presence of hard limits.It has been proved that hard limits can affectsystem stability.We find that (1) hard limits can change unstable equilibrium into stable one;(2) hard limits canchange stability of limit cycles induced by Hopf bifurcation;(3) persistence of hard limits can stabilize divergenttrajectory to a stable equilibrium or limit cycle;(4) Hopf bifurcation occurs before SN bifurcation,so the systemcollapse can be controlled before Hopf bifurcation occurs.We also find that suitable limiting values of hard limitscan enlarge the feasibility region.These results are based on theoretical analysis and numerical simulations,such as condition for SNB and Hopf bifurcation,bifurcation diagram,trajectories,Lyapunov exponent,Floquetmultipliers,dimension of attractor and so on. |
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| Keywords: | SMIB system Bifurcations chaos stability feasibility region |
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