Strong convergence and almost sure exponential stability of balanced numerical approximations to stochastic delay Hopfield neural networks

Anandaraman Rathinasamy and Pichamuthu Mayavel

Applied Mathematics and Computation, 2023, vol. 438, issue C

Abstract: This paper deals with the balanced numerical schemes of the stochastic delay Hopfield neural networks. The balanced methods have a strong convergence rate of at least 12 and the balanced schemes have almost sure exponential stability under certain conditions. Under the Lipchitz and linear growth conditions, the balanced Euler methods are proved to have a strong convergence of order 12 in mean-square sense. Using the Lipchitz conditions on the various parameters of the model, based on the semimartingale convergence theorem and some reasonable assumptions, the balanced Euler methods of the stochastic delay Hopfield neural networks are proved to be almost sure exponentially stable. Numerical experiments are provided to illustrate the theoretical results which are derived in this paper. The computational efficiency of the balanced methods is demonstrated by numerical tests and compared to the Euler–Maruyama approximation scheme of the stochastic delay Hopfield neural networks. Furthermore, the obtained numerical results show that the balanced numerical methods of stochastic delay Hopfield neural networks are very efficient with the least error and have the best step size region for almost sure mean square stable.

Keywords: Stochastic delay Hopfield neural networks; Balanced numerical schemes; Strong convergence; Almost sure exponential stable (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300322006476
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:438:y:2023:i:c:s0096300322006476

DOI: 10.1016/j.amc.2022.127573

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().