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Conditions for the Existence of Cycles in a System of Differential Equations

Conditions for the Existence of Cycles in a System of Differential Equations We consider a third-order differential system generalizing a system that describes amathematical model of the phase lock-in phenomenon. Sufficient conditions for the existence of asaddle cycle of the first kind for this system are obtained. The proof of the conditions is based onconstructing a positively invariant toroidal set using two cylindrical surfaces whose boundaries aredetermined by the limit cycles of a second-order differential system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Conditions for the Existence of Cycles in a System of Differential Equations

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References (10)

Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2022
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/s0012266122020033
Publisher site
See Article on Publisher Site

Abstract

We consider a third-order differential system generalizing a system that describes amathematical model of the phase lock-in phenomenon. Sufficient conditions for the existence of asaddle cycle of the first kind for this system are obtained. The proof of the conditions is based onconstructing a positively invariant toroidal set using two cylindrical surfaces whose boundaries aredetermined by the limit cycles of a second-order differential system.

Journal

Differential EquationsSpringer Journals

Published: Feb 1, 2022

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