Multispikes and synchronization in a large neural network with temporal delays

Coherent rhythms in the gamma frequency range are ubiquitous in the nervous system and thought to be important in a variety of cognitive activities. S uch rhythms are known to be able to synchronize with millisecond precision across distances with significant conduction delay; it is mysterious how th is can operate in a setting in which cells receive many inputs over a range of time. Here we analyze a version of mechanism, previously proposed, that the synchronization in the CA1 region of the hippocampus depends on the fi ring of "doublets" by the interneurons. Using a network of local circuits t hat are arranged in a possibly disordered lattice, we determine the conditi ons on parameters for existence and stability of synchronous solutions in w hich the inhibitory interneurons fire single spikes, doublets, or triplets per cycle. We show that the synchronous solution is only marginally stable if the interneurons fire singlets. If they fire doublets, the synchronous s tate is asymptotically stable in a larger subset of parameter space than if they fire triplets. An unexpected finding is that a small amount of disord er in the lattice structure enlarges the parameter regime in which the doub let solution is stable. Synaptic noise reduces the regime in which the doub let configuration is stable, but only weakly.