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首页> 外文期刊>Physical review, E >Emergence and analysis of Kuramoto-Sakaguchi-like models as an effective description for the dynamics of coupled Wien-bridge oscillators
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Emergence and analysis of Kuramoto-Sakaguchi-like models as an effective description for the dynamics of coupled Wien-bridge oscillators

机译：Kuramoto-Sakaguchi模型的出现与分析作为耦合Wien桥振荡器动态的有效描述

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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 an RC bandpass filter) and positive feedback (via an operational amplifier). In the past 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 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 the 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 of two coupled Wien-bridge oscillators and relate the results to the theoretical predictions.
机译：我们从管理两个耦合的Wien-Bridge振荡器的基本电路方程获得Kuramoto-Sakaguchi模型。 Wien-Bridge振荡器是可调谐自主振荡器的特定实现，其利用频率滤波（通过RC带通滤波器）和正反馈（通过运算放大器）。在过去几年中，这种振荡器已经开始在同步研究中使用。首先表明，可以以耦合的范德波极方程的形式铸造Wien桥接电路方程。随后，通过应用多个时间尺度的方法，我们导出控制振荡器阶段和幅度慢速演变的微分方程。这些方程直接让人想起Kuramoto-Sakaguchi型模型，用于研究同步。我们在各种耦合振荡器解决方案的存在和稳定性方面分析所产生的系统，并在此基础上解释它们的同步出现。相位幅度方程也与原始电路方程数数量进行比较，并且找到了良好的协议。最后，我们报告了两个耦合的Wien桥振荡器的实验测量，并将结果与​​理论预测相关。

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