Stability of Stochastic Delayed Recurrent Neural Networks

Hongying Xiao, Mingming Xu, Yuanyuan Zhang and Shengquan Weng ()
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Hongying Xiao: School of Mathematics and Physics, Yibin University, Yibin 644000, China
Mingming Xu: School of Mathematics and Physics, Yibin University, Yibin 644000, China
Yuanyuan Zhang: Department of Mathematics, China Three Gorges University, Yichang 443002, China
Shengquan Weng: School of Mathematics and Physics, Yibin University, Yibin 644000, China

Mathematics, 2025, vol. 13, issue 14, 1-18

Abstract: This paper addresses the stability of stochastic delayed recurrent neural networks (SDRNNs), identifying challenges in existing scalar methods, which suffer from strong assumptions and limited applicability. Three key innovations are introduced: (1) weakening noise perturbation conditions by extending diagonal matrix assumptions to non-negative definite matrices; (2) establishing criteria for both mean-square exponential stability and almost sure exponential stability in the absence of input; (3) directly handling complex structures like time-varying delays through matrix analysis. Compared with prior studies, this approach yields broader stability conclusions under weaker conditions, with numerical simulations validating the theoretical effectiveness.

Keywords: mean-square exponential input-to-state stability; mean-square exponential stability; almost sure exponential stability; Lyapunov functional; martingale convergence theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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