Integrated Stochastic Investigation of Singularly Perturbed Delay Differential Equations for the Neuronal Variability Model

Author:

Ahmad Iftikhar1ORCID,Hussain Syed Ibrar2ORCID,Ilyas Hira1ORCID,Zoubir Layouni3ORCID,Javed Mariam1,Zahoor Raja Muhammad Asif4ORCID

Affiliation:

1. Department of Mathematics, University of Gujrat, Gujrat, Pakistan

2. Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Via Archirafi 34, Palermo 90123, Italy

3. Department of SEG, University of Badji Mokhtar, Annaba, Algeria

4. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan

Abstract

The proposed research utilizes a computational approach to attain a numerical solution for the singularly perturbed delay differential equation (SPDDE) problem arising in the neuronal variability model through artificial neural networks (ANNs) with different solvers. The log-sigmoid function is used to construct the fitness function. The implementation of ANN on SPDDE problems is formulated for different solvers and trained with different weights. The optimization solvers such as the genetic algorithm (GA), sequential quadratic programming (SQP), and pattern search (PS) are hybridized with the active set technique (AST) and the interior-point technique (IPT) and is used to check the accuracy and rapid convergence of the numerical results of the SPDDE model. The numerical outcomes demonstrate that the system is easy to handle and efficient to solve with boundary conditions. Moreover, we used the mean residual error for one hundred runs for each solver to validate the accuracy of the proposed scheme.

Publisher

Hindawi Limited

Subject

Artificial Intelligence,Human-Computer Interaction,Theoretical Computer Science,Software

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