不对称达芬振荡器：1:2$共振的变形及其与主共振的相互作用

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-07-03 DOI:arxiv-2407.03423

Jan Kyziol, Andrzej Okniński

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引用次数: 0

摘要

我们研究了周期性受迫非对称杜芬振荡器中的 1: 2 美元共振，它是由于主 1: 1 美元共振的周期加倍或与主共振共存而独立形成的。我们计算了稳态渐近解--幅频隐函数。在隐函数微分性质框架下，我们描述了 1:2$ 共振的复杂变形及其与主共振的相互作用。

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

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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arXiv - PHYS - Chaotic Dynamics

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