Solitary Waves of Integrate-and-Fire Neural Fields

David Horn*, Irit Opher

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Arrays of interacting identical neurons can develop coherent firing patterns, such as moving stripes that have been suggested as possible explanations of hallucinatory phenomena. Other known formations include rotating spirals and expanding concentric rings. We obtain all of them using a novel two-variable description of integrate-and-fire neurons that allows for a continuum formulation of neural fields. One of these variables distinguishes between the two different states of refractoriness and depolarization and acquires topological meaning when it is turned into a field. Hence, it leads to a topologic characterization of the ensuing solitary waves, or excitons. They are limited to pointlike excitations on a line and linear excitations, including all the examples noted above, on a two-dimensional surface. A moving patch of firing activity is not an allowed solitary wave on our neural surface. Only the presence of strong inhomogeneity that destroys the neural field continuity allows for the appearance of patchy incoherent firing patterns driven by excitatory interactions.

Original languageEnglish
Pages (from-to)1677-1690
Number of pages14
JournalNeural Computation
Volume9
Issue number8
DOIs
StatePublished - 15 Nov 1997

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