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.
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Dedicated to the memory of Russell A. Johnson
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Both authors were partially supported by MICIIN/FEDER under Project RTI2018-096523-B-100.
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Kloeden, P.E., Villarragut, V.M. Sigmoidal Approximations of a Nonautonomous Neural Network with Infinite Delay and Heaviside Function. J Dyn Diff Equat 34, 721–745 (2022). https://doi.org/10.1007/s10884-020-09899-4
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DOI: https://doi.org/10.1007/s10884-020-09899-4
Keywords
- Neural networks
- Differential inclusion
- Nonautonomous set-valued dynamical system
- Pullback attractor
- Upper semi convergence