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arXiv · 2401.05387

Periodic second-order systems and coupled forced Van der Pol oscillators

Feliz Minhós·Sara Perestrelo
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Abstract

We present an existence and localization result for periodic solutions of second-order non-linear coupled planar systems, without requiring periodicity for the non-linearities. The arguments for the existence tool are based on a variation of the Nagumo condition and the Topological Degree Theory. The localization tool is based on a technique of orderless upper and lower solutions, that involves functions with translations. We apply our result to a system of two coupled Van der Pol oscillators with a forcing component.

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Feliz Minhós, Sara Perestrelo. 2023-12-18. Periodic second-order systems and coupled forced Van der Pol oscillators. https://arxiv.org/abs/2401.05387

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