Complex dynamics in winner-take-all neural nets with slow inhibition

-We consider a layer of excitatory neurons with small asymmetric excitatory connections and strong coupling to a single inhibitory interneuron. I f the inhibition is fast, the network behaves as a winner-take-all network in which one cell fires at the expense of all others. As the inhibition slows down, oscillatory behavior begins. This is followed by a symmetric rotating solution in which neurons share the activity in a round-robin fashion. Finally, i f the inhibition is sufficiently slower than excitation the neurons completely synchronize to a global periodic solution. Conditions guaranteeing stable synchrony are given. Keywords--Synchrony, Rhythmogenesis, Oscillatory neurons.