Propriedades de escala em um modelo com comportamento coletivo

Abstract

Developed for modeling the synchronization phenomenon, the Kuramoto model consists of a system of N-coupled oscillators with randomly distributed natural frequencies whose dynamics is described by a set of differential equations. Variations in number of oscillators and randomness imposed by distribution of natural frequencies induce changes in the synchronization process. In this work, a scale analysis on the number of oscillators and the dispersion parameter of natural frequencies of Normal, Cauchy-Lorentz and Laplace distributions was performed. It is shown in both cases that the synchronization, measured by the order parameter, obeys specifics scaling functions and, therefore, the number of oscillators and the order parameters are scalar invariants, i.e., they do not change qualitatively the synchronization. The proposed methodology can aid in the analysis of other parameters or models.