ERRATUM: A Center Manifold Result for Delayed Neural Fields Equations

Romain Veltz 1 Olivier Faugeras 1
1 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : Lemma C.1 in [R. Veltz and O. Faugeras, SIAM J. Math. Anal., 45(3) (2013), pp. 1527-1562] is wrong. This lemma is used in the proof of the existence of a smooth center manifold, Theorem 4.4 in [5]. An additional assumption is required to prove this existence. We spell out this assumption, correct the proofs and show that the assumption is satisfied for a large class of delay functions τ . We also weaken the general assumptions on τ .
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Romain Veltz, Olivier Faugeras. ERRATUM: A Center Manifold Result for Delayed Neural Fields Equations. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2015, ⟨10.1137/140962279⟩. ⟨hal-01096598⟩

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