Lyapunov functions in the global analysis of chaotic systems
We present an overview of development of the direct Lyapunov method in the global analysis of chaotic systems and describe three directions in which the Lyapunov functions are applied: in the methods of localization of global attractors, where the estimates of dissipativity in a sense of Levinson ar...
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| Datum: | 2018 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2018
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1541 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We present an overview of development of the direct Lyapunov method in the global analysis of chaotic systems and
describe three directions in which the Lyapunov functions are applied: in the methods of localization of global attractors,
where the estimates of dissipativity in a sense of Levinson are obtained, in the problems of existence of homoclinic
trajectories, and in the estimation of the dimension of attractors. The efficiency of construction of Lyapunov-type functions
is demonstrated. In particular, the Lyapunov dimension formula is proved for the attractors of the Lorentz system. |
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