  We consider a ring network of quadratic integrate-and-fire neurons with
nonlocal synaptic and gap junction coupling. The corresponding neural field
model supports solutions such as standing and travelling waves, and also
lurching waves. We show that many of these solutions satisfy self-consistency
equations which can be used to follow them as parameters are varied. We perform
numerical bifurcation analysis of the neural field model, concentrating on the
effects of varying gap junction coupling strength. Our methods are generally
applicable to a wide variety of networks of quadratic integrate-and-fire
neurons.
