Eur. Phys. J. Special Topics 165, 103-109 (2008)
https://doi.org/10.1140/epjst/e2008-00853-1

A linear path toward synchronization

Anomalous scaling in a new class of exactly solvable Kuramoto models

Center of Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, New Mexico, 87545, U.S.A.

Abstract

Using a recently introduced linear reformulation of the Kuramoto model of self-synchronizing oscillator systems [1], we study a new class of analytically solvable oscillator systems defined by a particular coupling scheme. We show that these systems have a logarithmic scaling law in the vicinity of the critical point, which may be seen as anomalous with respect to the usual power-law behavior exhibited by the standard Kuramoto model.