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arXiv · 2407.03423

Asymmetric Duffing oscillator: metamorphoses of $1:2$ resonance and its interaction with the primary resonance

Jan Kyziol·Andrzej Okniński
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Abstract

We investigate the $1: 2$ resonance in the periodically forced asymmetric Duffing oscillator due to the period-doubling of the primary $1: 1$ resonance or forming independently, coexisting with the primary resonance. We compute the steady-state asymptotic solution - the amplitude-frequency implicit function. Working in the differential properties of implicit functions framework, we describe complicated metamorphoses of the $1:2$ resonance and its interaction with the primary resonance.

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Jan Kyziol, Andrzej Okniński. 2024-07-03. Asymmetric Duffing oscillator: metamorphoses of $1:2$ resonance and its interaction with the primary resonance. https://arxiv.org/abs/2407.03423

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