The balanced numerical approximations of stochastic delay hopfield neural networks with poisson jumps

Abstract

This thesis focuses on two important aspects: almost sure newlineexponential stability and strong convergence, specifically in the context of newlinebalanced numerical approximations applied to stochastic delay Hopfield neural newlinenetworks. Stochastic differential equations are used to model various real-world newlinescenarios, such as population dynamics, financial systems, and neural networks. newlineOften, it s challenging to find explicit solutions to these equations. In this newlinethesis, we explore the applications of balanced numerical approximations in the newlinecontext of stochastic delay Hopfield neural networks, which have relevance in newlinereal-world situations. newlineThe thesis comprises four main parts. The first part serves as newlinean introduction, providing essential background and definitions related to newlinestochastic delay Hopfield neural networks. In the second part, we delve into the newlineanalysis of almost sure exponential stability and strong convergence of balanced newlinenumerical approximations applied to stochastic delay Hopfield neural networks. newline