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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.<\/jats:p>","DOI":"10.1137\/s0036139993257375","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T02:55:41Z","timestamp":1109213741000},"page":"220-241","source":"Crossref","is-referenced-by-count":12,"title":["Synchrony and Clustering in an Excitatory Neural Network Model with Intrinsic Relaxation Kinetics"],"prefix":"10.1137","volume":"55","author":[{"given":"Paul F.","family":"Pinsky","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,5]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1002\/ana.410010510"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511895401"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1143\/ptp\/89.2.313"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0150098"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.71.1280"},{"key":"R6","unstructured":"D. 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