Global attractivity criteria for a discrete-time Hopfield neural network model with unbounded delays via singular M−matrices

José J. Oliveira, Ana Sofia Teixeira

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves global attractivity under two regimes using M-matrices that need not be invertible. The candidate model’s proof for case (i) incorrectly assumes that M̂ is necessarily a nonsingular M-matrix and relies on inverse-positivity; this contradicts the paper’s results and examples where M̂ is singular yet attractivity still follows. Case (ii) in the model is closer in spirit but remains different from the paper’s approach. Overall, the paper’s argument is sound, while the model’s proof does not establish Theorem 3.4 as stated.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript presents clear, practically relevant global attractivity criteria for discrete-time Hopfield-type models with both leakage delays and infinite distributed delays. Its novelty lies in dispensing with invertibility of the comparison M–matrices in (i) and handling singular irreducible M–matrices in (ii). The proofs are mostly self-contained and avoid Lyapunov constructions. I recommend minor revisions to expand the proof of Theorem 3.4(ii) beyond “follows similarly,” and to restate the M–matrix property (Theorem 2.1) actually used in the contradiction step, thus improving readability and rigor for a broad audience.