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.

Published as:English, L.Q., David Mertens, Saidou Abdoulkary, C.B. Fritz, K. Skowronski, and P.G. Kevrekidis. Emergence and Analysis of Kuramoto-Sakaguchi-Like Models as an Effective Description for the Dynamics of Coupled Wien-bridge Oscillators. Physical Review. E 94, no. 6 (2016): 062212. This author post-print is made available on Dickinson Scholar with the permission of the publisher. For more information on the published version, visit APS's (American Physical Society) Website.