Forced frequency locking for differential equations with distributional forcings
This paper deals with forced frequency locking, i.e., the behavior of periodic solutions to autonomous differential equations under the influence of small periodic forcings. We show that, although the forcings are allowed to be discontinuous (e.g., step-function-like) or even distributional (e.g., D...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2018
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1545 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | This paper deals with forced frequency locking, i.e., the behavior of periodic solutions to autonomous differential equations
under the influence of small periodic forcings. We show that, although the forcings are allowed to be discontinuous (e.g.,
step-function-like) or even distributional (e.g., Dirac-function-like), the forced frequency locking happens as in the case
of smooth forcings, and we derive formulas for the locking cones and for the asymptotic phases as in the case of smooth
forcings. |
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