On Synchronization and Phase Locking in Strongly Coupled Systems of Planar Rotators
Jacek M. Kowalski
Ali Ansari
Paul S. Prueitt
Department of Mathematics, University of Texas at Arlington,
Robert L. Dawes
Martingale Research Corporation, Allen, TX
Gunther Gross
University of North Texas, Center for Network Neuroscience
Abstract
Strongly coupled, dissipative systems of planar rotators are considered with the dynamics described by the autonomous system 
where the nonlinear coupling 
depends on the phase differences 
of 
rotators. It is pointed out that the simplest mechanism of the asymptotic synchronization in such systems can be described in terms of relative equilibria in the 
dimensional phase space transverse with respect to the barycentric motion. Particular examples of systems with short-range and all to all interaction are considered and the stability problem discussed. The simple entrainment picture based upon the presence of relative equilibria is excluded for large systems with all to all interactions and randomly distributed frequencies 
. Recently reported critical behavior of the synchronization phenomenon in these systems must then have more complicated dynamic origin.
