The split step theta balanced numerical approximations of stochastic time varying Hopfield neural networks with distributed delays

Abstract

In this paper, split step theta balanced Euler approximations for stochastic time-varying delay Hopfield neural networks (HNN) with distributed delays are examined for their exponential stability and strong convergence. The primary goal of this study is to determine how the stochastic HNN time varying delay term affects the analysis of numerically almost sure exponential stability. It became apparent that numerical solutions for stochastic Hopfield neural networks with time-varying and distributed delay functions had not been thoroughly explored. Hence, our research focused on probing into the realms of strong convergence and almost sure exponential stability through the lens of split-step theta-balanced Euler approximations. We examine the stability qualities using the discrete semimartingale convergence theorem. Additionally, we developed the theoretical findings pertaining to the split-step theta balanced Euler approximations almost sure exponential stability analysis and the analysis of the strong convergence order 1/2 in the mean of the global error. The theoretical results are validated through numerical experimentation.

Keywords

• Stochastic time varying Hopfield neural networks
• Standard Wiener process
• Split step theta balanced Euler approximations
• Distributed delay
• Almost sure exponential stability
• Strong convergence