作为耦合文氏桥振子动力学有效描述的类Kuramoto-Sakaguchi模型的出现和分析
The emergence and analysis of Kuramoto-Sakaguchi-like models as an effective description for the dynamics of coupled Wien-bridge oscillators
摘要：
我们推导出Kuramoto-Sakaguchi模型的基本电路方程控制两个耦合的维恩桥振荡器。维恩电桥振荡器是可调谐自主振荡器的一种特殊实现，它利用频率滤波（通过RC带通滤波器）和正反馈（通过运算放大器）。在过去的几年中，这种振荡器已开始被用于同步研究。我们首先表明，文氏电桥电路方程可以铸造的形式耦合对的Duffing-Van der Pol方程。随后，通过应用多时间尺度的方法，我们推导出的微分方程的振荡器的相位和振幅的缓慢演变。这些方程直接让人联想到用于研究同步的Kuramoto-Sakaguchi型模型。我们分析所产生的系统中的各种耦合振荡器的解决方案的存在性和稳定性，并解释在此基础上如何出现他们的同步。的相位-振幅方程也比较数值的原始电路方程，并发现良好的协议。最后，我们报告的实验测量两个耦合的维恩桥振荡器和相关的结果回到理论预测。
英文摘要：
We derive the Kuramoto-Sakaguchi model from the basic circuit equations governing two coupled Wien-bridge oscillators. A Wien-bridge oscillator is a particular realization of a tunable autonomous oscillator that makes use of frequency filtering (via a RC band-pass filter) and positive feedback (via an Op-Amp). In the last few years, such oscillators have started to be utilized in synchronization studies. We first show that the Wien-bridge circuit equations can be cast in the form of a coupled pair of Duffing - Van der Pol equations. Subsequently, by applying the method of multiple time scales, we derive the differential equations that govern the slow evolution of the oscillator phases and amplitudes. These equations are directly reminiscent of the Kuramoto-Sakaguchi type models for the study of synchronization. We analyze the resulting system in terms of existence and stability of various coupled oscillator solutions and explain on that basis how their synchronization emerges. The phase-amplitude equations are also compared numerically to the original circuit equations, and good agreement is found. Finally, we report on experimental measurements on two coupled Wien-bridge oscillators and relate the results back to the theoretical predictions.
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。
