New methods for the investigation of periodic solutions in ring systems of unidirectionally coupled oscillators
We consider special systems of ordinary differential equations, namely, ring systems of unidirectionally coupled oscillators. A new method is developed for the investigation of the problem of the existence and stability of periodic solutions for this class of systems. The specific feature of this ap...
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| Date: | 2013 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2013
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2406 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We consider special systems of ordinary differential equations, namely, ring systems of unidirectionally coupled oscillators.
A new method is developed for the investigation of the problem of the existence and stability of periodic solutions for this
class of systems. The specific feature of this approach is the use of certain auxiliary delay systems for the determination of
cycles and for the analysis of their properties. The proposed method is illustrated by a specific example. |
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