Artículos de revistas
Local attractors, degeneracy and analyticity: Symmetry effects on the locally coupled Kuramoto model
Date
2013-04-02Registration in:
Chaos, Solitons and Fractals, v. 49, n. 1, p. 32-46, 2013.
0960-0779
10.1016/j.chaos.2013.02.008
WOS:000318260900006
2-s2.0-84875419076
Author
Universidade Estadual Paulista (Unesp)
Universidade de São Paulo (USP)
Institutions
Abstract
In this work we study the local coupled Kuramoto model with periodic boundary conditions. Our main objective is to show how analytical solutions may be obtained from symmetry assumptions, and while we proceed on our endeavor we show apart from the existence of local attractors, some unexpected features resulting from the symmetry properties, such as intermittent and chaotic period phase slips, degeneracy of stable solutions and double bifurcation composition. As a result of our analysis, we show that stable fixed points in the synchronized region may be obtained with just a small amount of the existent solutions, and for a class of natural frequencies configuration we show analytical expressions for the critical synchronization coupling as a function of the number of oscillators, both exact and asymptotic. © 2013 Elsevier Ltd. All rights reserved.