Pattern Formation in an Array of Oscillators with Electrical and Chemical Coupling

Weak coupling theory is applied to a model for firing waves in the procerebral lobe of the slug. Inhibitory synapses and electrical synapses have different synchronizing properties. We show that, in concert, these two types of coupling can cause a bifurcation to a patterned state from synchrony which ultimately develops into traveling waves. Normal forms for the bifurcation are computed, and the results are compared to numerical simulations of the phase models.