English

Sigmoidal approximations of a nonautonomous neural network with infinite delay and Heaviside function

Dynamical Systems 2024-02-01 v1

Abstract

In this paper, we approximate a nonautonomous neural network with infinite delay and a Heaviside signal function by neural networks with sigmoidal signal functions. We show that the solutions of the sigmoidal models converge to those of the Heaviside inclusion as the sigmoidal parameter vanishes. In addition, we prove the existence of pullback attractors in both cases, and the convergence of the attractors of the sigmoidal models to those of the Heaviside inclusion.

Cite

@article{arxiv.2401.17936,
  title  = {Sigmoidal approximations of a nonautonomous neural network with infinite delay and Heaviside function},
  author = {Peter E. Kloeden and V. M. Villarragut},
  journal= {arXiv preprint arXiv:2401.17936},
  year   = {2024}
}

Comments

27 pages

R2 v1 2026-06-28T14:33:14.662Z