| 动力系统中的Lipschitz稳定性 |
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| 引用本文： | 陈文成.动力系统中的Lipschitz稳定性[J].数学学报,1995,38(5):621-627. |
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| 作者姓名： | 陈文成 |
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| 作者单位： | 山东矿业学院应用数学系 |
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| 摘 要： | 本文讨论动力系统的Ｌｉｐｓｃｈｉｔｚ稳定性与吸引性之间的关系．给出动力系统中弱吸引性、吸引性和强吸引性这三个概念相互等价的条件，在一定的条件下证明了（弱、强）吸引子与全局（弱、强）吸引子是一致的．本文还讨论了度量Ｌｙａｐｕｎｏｖ稳定性和拓扑Ｌｙａｐｕｎｏｖ稳定性及它们与Ｌｉｐｓｃｈｉｔｚ稳定性之间的关系．
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| 关 键 词： | 动力系统，正Lipschitz稳定性，正向极限集，正向延伸极限集，吸引子，度量Lyapunov稳定性 |
| 收稿时间： | 1994-7-16 |
Lipschitz Stability in Dynamical Systems |
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| ChenWencheng.Lipschitz Stability in Dynamical Systems[J].Acta Mathematica Sinica,1995,38(5):621-627. |
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| Authors: | ChenWencheng |
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| Institution: | ChenWencheng(Institute of Mathematics ,Academia Sinica ,Beijing 100080, China) |
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| Abstract: | The main purpose of this papet is to discuss the relationship between attraction andLipschitz stability in dynamical systems. Some conditions are given for the pairwise equivalencesamong the three notions of weak attraction,attraction and strong attraction. Under certainconditions, it is shown that the notions of an(a Weak,strong)attractor and a global(weak,strong)attractor coincide .Also, we investigate the metric and topological Lyapunov stability and their relations with Lipschitz stability. |
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| Keywords: | dynamical system positive Lipschitz stability positive limit set positive prolonga-tional limit set attractor metric Lyapunov stability |
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