通过参数调制极限环振子中的非线性来抑制双节律性
Suppressing birhythmicity by parametrically modulating nonlinearity in limit cycle oscillators
摘要：
振荡器中的多节律性，即多稳定性的一种形式，是一种在许多科学分支中都发现的有趣现象。从应用的角度来看，虽然多节律性有时是可取的，因为它为我们提供了许多可能共存的稳定振荡状态，但它也可能是一种滋扰，因为随机扰动可能使系统稳定在不需要的稳定状态。因此，有许多自然和人工机制可以控制多节律性并不奇怪。在本文中，我们提出了将参数（周期性）调制的非线性阻尼的极限环振荡器的想法，以期激发共振和反共振响应在特定的角驱动频率，并通过改变调制的振幅控制所产生的birrhythicity。为此，我们采用分析（微扰）和数值技术的范德波尔振荡器-一个范例的极限环系统-具有额外的位置依赖的时间延迟项和其修改后的自主birrhythmic版本。我们还提出了这样一个事实，即延迟-一种常用的控制多节律性的方法-在这样一个系统中，有时会带来不必要的birrhythmicity的介绍，有趣的是，我们的方法控制birrhythmicity通过周期性调制可以抑制这种延迟诱导的birrhythmic反应。
英文摘要：
Multirhythmicity, a form of multistability, in an oscillator is an intriguing phenomenon found across many branches of science. From an application point of view, while the multirhythmicity is sometimes desirable as it presents us with many possible coexisting stable oscillatory states to tap into, it can also be a nuisance because a random perturbation may make the system settle onto an unwanted stable state. Consequently, it is not surprising that there are many natural and artificial mechanisms available that can control the multirhythmicity. We propose in this paper the idea of incorporating parametric (periodic) modulation of the nonlinear damping in the limit cycle oscillators with a view to exciting resonance and antiresonance responses at particular angular driving frequencies, and controlling the resulting birhythmicity by changing the amplitude of the modulation. To this end, we employ analytical (perturbative) and numerical techniques on the van der Pol oscillator---a paradigmatic limit cycle system---having additional position dependent time delay term and its modified autonomous birhythmic version. We also bring the fact to the fore that introduction of delay---a commonly adopted method of controlling multirhythmicity---in such a system can sometimes bring forth unwanted birhythmicity; and interestingly, our method of controlling birhythmicity through periodic modulation can suppress such a delay induced birhythmic response.
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