Features of a rich attractor space in a system of repulsively coupled Kuramoto oscillators

Rhythmic behaviors with a wide range of periods emerge from populations of coupled oscillators in many phenomena in nature. The Kuramoto model is one of the simplest models of coupled oscillators vastly used to explain many such phenomena. Choosing a repulsive coupling and a proper topology in this model leads to frustration and, as a result, versatile features of multistability. Also, by choosing non-homogeneous natural frequencies, in a large enough system orbits emerge with very long periods that are 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.