  We study rotating waves in the Theta model for a ring of
synaptically-interacting neurons. We prove that when the neurons are
oscillatory, at least one rotating wave always exists. In the case of excitable
neurons, we prove that no travelling waves exist when the synaptic coupling is
weak, and at least two rotating waves, a `fast' one and a `slow' one, exist
when the synaptic coupling is sufficiently strong. We derive explicit upper and
lower bounds for the `critical' coupling strength as well as for wave
velocities. We also study the special case of uniform coupling, in which
complete analytical results on the rotating waves can be achieved.
