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. If 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, if the inhibition is sufficiently slower than excitation the neurons completely synchronize to a global periodic solution. Conditions guaranteeing stable synchrony are given.