title: Phase transitions in the Kuramoto model.
abstract: We consider the Kuramoto model of phase oscillators with natural frequencies distributed according to a unimodal function with the plateau section in the middle representing the maximum and symmetric tails falling off predominantly as |omega-omega0|m, m>0, in the vicinity of the flat region. It is found that the phase transition is of first order as long as there is a finite flat region and that in the vicinity of the critical coupling the following scaling law holds r-rc proportional, variant(K-Kc)2/(2m+3), where r is the order parameter and K is the coupling strength of the interacting oscillators.
authors.affiliation: Faculty of Electrical Engineering and Information Technologies, SS. Cyril and Methodius University, P.O. Box 574, Skopje, Macedonia. lasko@feit.ukim.edu.mk
authors.forename: Lasko
authors.initials: L
authors.lastname: Basnarkov
authors.forename: Viktor
authors.initials: V
authors.lastname: Urumov