Projeto, Construção e Modelagem Não Linear do Oscilador de Quadratura

Abstract

The study of networks of coupled oscillators enables the development of a broad range of methods for the analysis and control of complex systems. The Kuramoto model stands out as a dynamical model for synchronization analysis in the field. This paper proposes the implementation of an electronic circuit, the quadrature oscillator, to represent and analyze the dynamical behavior of a Kuramoto oscillator in an experimental setting in which external noise and parametric uncertainties are ubiquotously present. Other circuits have been proposed for this purpose, but they lack robust regulation of the oscillation amplitude. We developed a nonlinear model of the circuit (in contrast to previously developed linear models), along with its electronic design, construction, and validation. The results exhibit strong agreement between the model and experiments, providing new perspectives for the utilization of these oscillators in studies of complex networks.