Dynamics of Coupled Oscillator Systems - Abstract
In this talk, we discuss the emergence and co-existence of stable patterns of synchrony in two- and three- population networks of identical Kuramoto oscillators with inertia. The populations have different sizes and can split into clusters where the oscillators synchronize within a cluster while there is a phase shift between the dynamics of the clusters. Due to the presence of inertia, which increases the dimensionality of the oscillator dynamics, this phase shift can oscillate periodically or chaotically, inducing a chaotically breathing cluster pattern. We derive analytical conditions for the co-existence of stable patterns with constant and oscillating phase shifts in two- and three-population networks. We demonstrate that the multistable, and possibly, chaotic dynamics of the phase shifts in the three-population network is governed by two coupled driven pendulum equations. We also discuss the implications of our stability results to the stability of chimeras.