Phase equations for quasi-periodic oscillators

Abstract

Oscillations and rhythmic activity are seen in natural and man-made systems. Dynamics of oscillators can be compactly described by phase domain models. Phase equations for periodic, single-frequency oscillators have been developed and utilized in analyzing oscillation phenomena that arise in electronic systems, circadian clocks, and the nervous system. We consider quasi-periodic oscillators and present a general phase model theory and numerical techniques for the construction of phase equations for multi-frequency oscillators. We demonstrate the utility of these phase equations in analyzing oscillators experiencing perturbations.