Disorder-induced dynamics in a pair of coupled heterogeneous phase oscillator networks

We consider a pair of coupled heterogeneous phase oscillator networks and investigate their dynamics in the continuum limit as the intrinsic frequencies of the oscillators are made more and more disparate. The Ott/Antonsen Ansatz is used to reduce the system to three ordinary differential equations. We find that most of the interesting dynamics, such as chaotic behaviour, can be understood by analysing a gluing bifurcation of periodic orbits; these orbits can be thought of as "breathing chimeras" in the limit of identical oscillators. We also add Gaussian white noise to the oscillators' dynamics and derive a pair of coupled Fokker-Planck equations describing the dynamics in this case. Comparison with simulations of finite networks of oscillators is used to confirm many of the results.