Travelling waves in arrays of delay-coupled phase oscillators.

We consider the effects of several forms of delays on the existence and stability of travelling waves in non-locally coupled networks of Kuramoto-type phase oscillators and theta neurons. By passing to the continuum limit and using the Ott/Antonsen ansatz, we derive evolution equations for a spatially dependent order parameter. For phase oscillator networks, the travelling waves take the form of uniformly twisted waves, and these can often be characterised analytically. For networks of theta neurons, the waves are studied numerically.