A center manifold result for delayed neural fields equations

Romain Veltz (1) , Olivier Faugeras (1)

1 NEUROMATHCOMP - Neurosciences Mathématique et Computationnelle

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 impossible 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 etal. together with a theory of linear functional differential equations in a history space larger than the commonly used set of time-continuous functions.

Domaines: Analyse fonctionnelle [math.FA]

Romain Veltz, Olivier Faugeras. A center manifold result for delayed neural fields equations. [Research Report] RR-8020, 2012. ⟨hal-00719794v1⟩