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arXiv · 2503.13394

On the formation of the 1:2 resonance in oscillator dynamics

Jan Kyzioł·Andrzej Okniński
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Abstract

The dynamics of nonlinear oscillators are investigated. We study the formation of $1:2$ resonance in nonlinear periodically forced oscillators due to period doubling of the primary $1:1$ resonance, or born independently. We compute the amplitude-frequency implicit function, the steady-state asymptotic solution, for the effective equation approximating coupled oscillators. Working in the framework of differential properties of implicit functions, we demonstrate that birth of $1:2$ resonances corresponds to singular isolated points of the implicit functions. We provide numerical examples illustrating our theoretical findings.

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Jan Kyzioł, Andrzej Okniński. 2025-03-17. On the formation of the 1:2 resonance in oscillator dynamics. https://doi.org/10.1115/1.4070682

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