Almost sure exponential numerical stability of balanced Maruyama with two step approximations of stochastic time delay Hopfield neural networks

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Kopperundevi Sivarajan

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Journal Paper

Paper Information

Journal: Computational Methods for Differential Equations Year:2024 | Volume:12 | Issue:1 Page(s): 136-148

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Title

Almost sure exponential numerical stability of balanced Maruyama with two step approximations of stochastic time delay Hopfield neural networks

Author(s)

Kopperundevi Sivarajan | Issue Writer Certificate

Keywords

Almost sure exponential stability

balanced two step Maruyama numerical approximations

Hopfield neural networks

Stochastic delay differential equations

Abstract

This study examines the balanced Maruyama with two step approximations of stochastic Hopfield neural networks with delay. The main aim of this paper is to discover the conditions under which the exact solutions remain stable for the balanced Maruyama with two-step approximations of stochastic delay Hopfield neural networks (SDHNN). The semi martingale theorem for convergence is used to demonstrate the Almost sure exponential stability of balanced Maruyama with two-step approximations of stochastic delay Hopfield networks. Additionally, the numerical balanced Euler approximation's stability conditions are compared. Our theoretical findings are illustrated with numerical experiments.

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