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

Grégory Faye 1
1 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
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.
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Submitted on : Wednesday, July 17, 2013 - 2:13:30 PM
Last modification on : Monday, September 10, 2018 - 10:28:06 AM

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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, Elsevier, 2012, 350 (3-4), pp.161--166. ⟨10.1016/j.crma.2012.01.022⟩. ⟨hal-00845587⟩

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