非对称Duffing振子：$1:2$共振的变形及其与主共振的相互作用
Asymmetric Duffing oscillator: metamorphoses of $1:2$ resonance and its interaction with the primary resonance
AI总结：
本文研究非对称Duffing振子中$1:2$共振的变形及其与主共振的相互作用，通过计算幅频隐函数并利用隐函数微分性质揭示其复杂动力学行为。
摘要：
我们研究了周期强迫的非对称Duffing振子中的$1:2$共振，该共振可能由主$1:1$共振的倍周期分岔产生，也可能独立形成，并与主共振共存。我们计算了稳态渐近解——幅频隐函数。在隐函数的微分性质框架下，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。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
