Correlated disorder in the Kuramoto model: Effects on phase coherence, finite-size scaling, and dynamic fluctuations.
We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction p of oscillators are positively coupled, attracting all others, while the remaining fraction 1-p are negatively coupled, repelling all others. The frequencies and couplings are deterministically chosen in a manner which correlates them, thereby correlating the two types of disorder in the model. We first explore the effect of this correlation on the system's phase coherence. We find that there is a critical width γcin the frequency distribution below which the system spontaneously synchronizes. Moreover, this γcis independent of p. Hence, our model and the traditional Kuramoto model (recovered when p = 1) have the same critical width γc. We next explore the critical behavior of the system by examining the finite-size scaling and the dynamic fluctuation of the traditional order parameter. We find that the model belongs to the same universality class as the Kuramoto model with deterministically (not randomly) chosen natural frequencies for the case of p < 1.
Department of Physics and Research Institute of Physics and Chemistry, Chonbuk National University, Jeonju 561-756, South Korea.
Hyunsuk
H
Hong
Center for Applied Mathematics, Cornell University, Ithaca, New York 14853, USA.
Kevin P
KP
O'Keeffe
Department of Mathematics, Cornell University, Ithaca, New York 14853, USA.
Steven H
SH
Strogatz