title: Emergence and analysis of Kuramoto-Sakaguchi-like models as an effective description for the dynamics of coupled Wien-bridge oscillators.
abstract: 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.
authors.affiliation: Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA.
authors.forename: L Q
authors.initials: LQ
authors.lastname: English
authors.affiliation: Department of Physics, Eckerd College, St. Petersburg, Florida 33711, USA.
authors.forename: David
authors.initials: D
authors.lastname: Mertens
authors.affiliation: Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA.|Département des Sciences Fondamentales, de Droit et des Humanités, IMIP University of Maroua, P.O. Box 46, Maroua, Cameroon.|Laboratory of Mechanics, Department of Physics, University of Yaoundé I, Yaoundé, Cameroon.
authors.forename: Saidou
authors.initials: S
authors.lastname: Abdoulkary
authors.affiliation: Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA.
authors.forename: C B
authors.initials: CB
authors.lastname: Fritz
authors.affiliation: Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA.
authors.forename: K
authors.initials: K
authors.lastname: Skowronski
authors.affiliation: Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA.
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis