  A common model to study pattern formation in large groups of neurons is the
neural field. We investigate a neural field with excitatory and inhibitory
neurons, like Wilson and Cowan (1972), with transmission delays and gap
junctions. We build on the work of Visser et al. (2017) by investigating
pattern formation in these models on the sphere. Specifically, we investigate
how different amounts of gap-junctions, modelled by a diffusion term, influence
the behaviour of the neural field. We look in detail at the periodic orbits
which are generated by Hopf bifurcation in the presence of spherical symmetry.
For this end, we derive general formulas to compute the normal form
coefficients of these bifurcations up to third order and predict the stability
of the resulting branches, and formulate a novel numerical method to solve
delay equations on the sphere.
