论文标题
高频激发次谐波夹带和限制周期调制：重新归一化的方法
Subharmonic entrainment and limit cycle modulation by high frequency excitation: A Renormalization group approach
论文作者
论文摘要
在本文中，我们探讨了在范式脱落的振荡器中使用两个频率激发的次谐波$（1 {：} 2）$夹带和超临界的Hopf分叉的可能性，其中包括一个慢速的参数驱动器和快速的外部强迫，并通过外部外部快速信号的振幅变化。我们还推断出产生亚谐波振荡所需的阈值参数强度的条件。 Blekhman扰动（运动的直接划分）和重新归一化组技术已被用来研究信号振幅如何在调节极限循环动力学以及亚谐波产生中起关键作用。通常通过将快速驱动器的强度作为控制参数来完成对此类驱动非线性系统的非线性响应和分叉的研究。在这里，我们表明，除了它在允许一个人以慢速分离的慢速和快速组件研究中的作用外，高频信号的幅度还可以视为控制极限循环行为和振荡器中亚旋转振荡的独立控制参数。我们的分析估计得到了数值模拟的很好的支持。
In this article, we explore the possibility of a sub-harmonic $(1{:}2)$ entrainment and supercritical Hopf bifurcation in a van der Pol-Duffing oscillator that has been excited by two frequencies, comprising a slow parametric drive and a fast external forcing, through the variation of the amplitude of the external fast signal. We also deduce the condition for the threshold parametric strength required to generate sub-harmonic oscillation. The Blekhman perturbation (direct partition of motion) and the Renormalization group technique have been employed to study how the signal amplitude plays a pivotal role in modulating the limit cycle dynamics as well as the subharmonic generation. Studies of nonlinear responses and bifurcations of such driven nonlinear systems are usually done by treating the strength of the fast drive as the control parameter. Here we show that, beyond its role in allowing one to study the dynamics with the slow and fast components nicely separated, the amplitude of the high-frequency signal can also be treated as an independent control parameter for controlling both the limit cycle behavior and the onset of subharmonic oscillation in the oscillator. Our analytical estimations are well supported by numerical simulations.
