A Center Manifold Result for Delayed Neural Fields Equations

Romain Veltz 1, * Olivier Faugeras 1
* Corresponding author
1 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : We develop a framework for the study of delayed neural fields equations and prove a center manifold theorem for these equations. Specific properties of delayed neural fields equations make it difficult to apply existing methods from the literature concerning center manifold results for functional differential equations. Our approach for the proof of the center manifold theorem uses the original combination of results from Vanderbauwhede et al. together with a theory of linear functional differential equations in a history space larger than the commonly used set of time-continuous functions
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Submitted on : Tuesday, August 6, 2013 - 1:06:54 PM
Last modification on : Friday, April 19, 2019 - 1:30:08 PM

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Romain Veltz, Olivier Faugeras. A Center Manifold Result for Delayed Neural Fields Equations. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2013, 45 (3), pp.1527-1562. ⟨10.1137/110856162⟩. ⟨hal-00850382⟩

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