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

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.