频率切换力驱动的振荡器中的新的慢-快行为
Novel slow-fast behaviour in an oscillator driven by a frequency-switching force
摘要：
当振荡器在不同频率之间突然切换时，在决定如何在切换时对系统进行建模时存在一些模糊性。在这里，我们描述了两个看似自然的模型的开关在一个简单的受迫谐振子，这完全不同意他们的预测，其长期的行为。试图通过“正则化”开关来解决分歧，不仅保留了分歧，而且表明它随着时间的推移而增加。其中一个模型对应于一个传统的“Filippov”描述的非光滑系统，而第二个表现出的结构，不可逆的年龄，开发了一些新的多尺度行为，我们相信还没有被报道过。这些包括慢-快楼梯，新颖的混合模式振荡，和一个同步鸭式爆炸。这些功能被证明是存在的使用渐近分析，但由于它们涉及一个慢-快的时间尺度分离，随着时间的推移而增加，它们超出了数值方法的范围。
英文摘要：
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple periodically-forced harmonic oscillator, which disagree starkly in their predictions of its long time behaviour. Attempting to resolve the disagreement by `regularizing' the switch not only preserves the disagreement, but shows it increases with time. One of the models corresponds to a conventional `Filippov' description of a nonsmooth system, while the second exhibits a structure that irreversibly ages, developing a number of novel multi-scale behaviours that we believe have not been reported before. These include slow-fast staircases, novel mixed-mode oscillations, and a synchronized canard explosion. These features are proven to exist using asymptotic analysis, but as they involve a slow-fast time-scale separation that increases with time, they lie beyond the reach of numerical methods.
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。
