Corrigendum to “Sigmoidal approximations of Heaviside functions in neural lattice models” [J. Differ. Equ. 268 (9) (2020) 5283–5300

Abstract

In [3] the solutions of a sigmoidal neural field lattice system based on an Amari-Hopfield neural field lattice model, in which the Heaviside function is replaced by a simplifying sigmoidal function characterized by a small parameter ε, were shown to converge to the solution of the Heaviside lattice system as ε→0, through an inflated lattice system which contains both of them. It was incorrectly claimed in the proof of Theorem 4 in [3] that the derivatives converge strongly in L1([0,T],R) rather than weakly. The proof is corrected here using the Banach-Saks theorem.