  We study the macroscopic dynamics of large networks of excitable type 1
neurons composed of two populations interacting with disparate but symmetric
intra- and inter-population coupling strengths. This nonuniform coupling scheme
facilitates symmetric equilibria, where both populations display identical
firing activity, characterized by either quiescent or spiking behavior, or
asymmetric equilibria, where the firing activity of one population exhibits
quiescent but the other exhibits spiking behavior. Oscillations in the firing
rate are possible if neurons emit pulses with non-zero width but are otherwise
quenched. Here, we explore how collective oscillations emerge for two
statistically identical neuron populations in the limit of an infinite number
of neurons. A detailed analysis reveals how collective oscillations are born
and destroyed in various bifurcation scenarios and how they are organized
around higher codimension bifurcation points. Since both symmetric and
asymmetric equilibria display bistable behavior, a large configuration space
with steady and oscillatory behavior is available. Switching between
configurations of neural activity is relevant in functional processes such as
working memory and the onset of collective oscillations in motor control.
