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- W2000580192 abstract "Synchronized firing of a population of neurons in the hippocampus has been studied as a model for epilepsy. This paper formulates an abstract model of an excitatory neural network which is qualitatively derived from a biophysical model of hippocampal neurons. In this model the phase space of an isolated neuron is a cylinder $( theta ,z )$; an additional variable s conveys the effects of excitatory coupling between cells. A small parameter $epsilon $ is introduced which represents the ratio of two time scales intrinsic to each neuron. It is proved that under certain conditions this model will possess stable approximately synchronous solutions; these are periodic or quasi-periodic solutions in which all cells fire approximately simultaneously (i.e., within a time interval of duration $O( epsilon )$ relative to the intrinsic cell period). These approximately synchronous solutions persist in the face of cell heterogeneity of magnitude $O( 1 )$. In the case where the network is homogenous, stable approximately synchronous solutions may exist even when the homogeneous solution is technically unstable. Various cluster states in which cells within a cluster fire approximately synchronously are also discussed." @default.
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- W2000580192 date "1995-02-01" @default.
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- W2000580192 title "Synchrony and Clustering in an Excitatory Neural Network Model with Intrinsic Relaxation Kinetics" @default.
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- W2000580192 doi "https://doi.org/10.1137/s0036139993257375" @default.
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