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Reports (Research Report) Year : 2007

Bumps in simple two-dimensional neural field models

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1
Olivier Faugeras

Abstract

Neural field models first appeared in the 50's, but the theory really took off in the 70's with the works of Wilson and Cowan {wilson-cowan:72,wilson-cowan:73} and Amari {amari:75,amari:77}. Neural fields are continuous networks of interacting neural masses, describing the dynamics of the cortical tissue at the population level. In this report, we study homogeneous stationary solutions (i.e independent of the spatial variable) and bump stationary solutions (i.e. localized areas of high activity) in two kinds of infinite two-dimensional neural field models composed of two neuronal layers (excitatory and inhibitory neurons). We particularly focus on bump patterns, which have been observed in the prefrontal cortex and are involved in working memory tasks {goldman-rakic:95}. We first show how to derive neural field equations from the spatialization of mesoscopic cortical column models. Then, we introduce classical techniques borrowed from Coombes {coombes:05} and Folias and Bressloff {folias-bressloff:04} to express bump solutions in a closed form and make their stability analysis. Finally we instantiate these techniques to construct stable two-dimensional bump solutions.
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Dates and versions

inria-00192952 , version 1 (29-11-2007)
inria-00192952 , version 2 (03-12-2007)
inria-00192952 , version 3 (17-01-2008)

Identifiers

  • HAL Id : inria-00192952 , version 3

Cite

Olivier Faugeras, François Grimbert. Bumps in simple two-dimensional neural field models. [Research Report] RR-6375, INRIA. 2007, pp.19. ⟨inria-00192952v3⟩
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