Matrix analysis
Introduction to the theory of neural computation
Introduction to the theory of neural computation
Alternating and synchronous rhythms in reciprocally inhibitory model neurons
Neural Computation
What matters in neuronal locking?
Neural Computation
Spikes: exploring the neural code
Spikes: exploring the neural code
Neuronal Networks of the Hippocampus
Neuronal Networks of the Hippocampus
Type i membranes, phase resetting curves, and synchrony
Neural Computation
Diffusion associative network: diffusive hybrid neuromodulation and volume learning
IWANN'03 Proceedings of the Artificial and natural neural networks 7th international conference on Computational methods in neural modeling - Volume 1
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Coherent rhythms in the gamma frequency range are ubiquitous in the nervous system and thought to be important in a variety of cognitive activities. Such rhythms are known to be able to synchronize with millisecond precision across distances with significant conduction delay; it is mysterious how this 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 firing of “doublets” by the interneurons. Using a network of local circuits that are arranged in a possibly disordered lattice, we determine the conditions on parameters for existence and stability of synchronous solutions in which 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 state is asymptotically stable in a larger subset of parameter space than if they fire triplets. An unexpected finding is that a small amount of disorder in the lattice structure enlarges the parameter regime in which the doublet solution is stable. Synaptic noise reduces the regime in which the doublet configuration is stable, but only weakly.