EE03: V: ICTP-SAIFR Satellite Session on Complex Systems

Tue. March 5, 11:30 a.m. – 11:50 a.m. CST

Virtual Room 03

Synchronization is a phenomenon found in many natural and artificial systems, from fireflies and pacemaker cells in the heart to metronomes and power grids. The model developed by Kuramoto became a paradigm in the field and has been studied and modified in many ways. One recent extension has generalized the model to more dimensions, where particles are allowed to move on the surface of spheres and are represented by unit vectors. In this talk I will argue that, in this setup, the coupling constant can be naturally extended to a coupling matrix acting on the vectors. The matrix breaks the rotational symmetry and results in a kind of generalized frustration that includes the Kuramoto-Sakaguchi model. I will show analytical results for identical oscillators in arbitrary dimensions and for Lorentz distributed oscillators in D=2.