Features of multistability in a system of repulsively coupled Kuramoto oscillators*

Coupled oscillators and emergent synchronized patterns are observed in many phenomena in nature. The Kuramoto model is one of  the simplest models of coupled oscillators that can explain many such phenomena. A proper choice of (repulsive) coupling constants and topology in this model leads to versatile features of multistability.  In particular, by choosing non-homogeneous natural frequencies long period orbits emerge, orders of magnitude longer than the natural frequencies. To understand the characteristics of the phase space we study the effects of tuning parameters like the coupling constant and the width of the frequency distribution.