Reduction method for studying localized solutions of neural field equations on the Poincaré disk - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Comptes rendus de l'Académie des sciences. Série I, Mathématique Year : 2012

Reduction method for studying localized solutions of neural field equations on the Poincaré disk

Grégory Faye

Abstract

We present a reduction method to study localized solutions of an integrodifferential equation defined on the Poincaré disk. This equation arises in a problem of texture perception modeling in the visual cortex. We first derive a partial differential equation which is equivalent to the initial integrodifferential equation and then deduce that localized solutions which are radially symmetric satisfy a fourth order ordinary differential equation.

Dates and versions

hal-00845587 , version 1 (17-07-2013)

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Grégory Faye. Reduction method for studying localized solutions of neural field equations on the Poincaré disk. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2012, 350 (3-4), pp.161--166. ⟨10.1016/j.crma.2012.01.022⟩. ⟨hal-00845587⟩
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