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Mathematics
Volume 13
Issue 14
10.3390/math13142310
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Stability of Stochastic Delayed Recurrent Neural Networks

by
Hongying Xiao
1,
Mingming Xu
1,
Yuanyuan Zhang
2 and
Shengquan Weng
1,*
1
School of Mathematics and Physics, YiBin University, Yibin 644000, China
2
Department of Mathematics, China Three Gorges University, Yichang 443002, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(14), 2310; https://doi.org/10.3390/math13142310 (registering DOI)
Submission received: 22 May 2025 / Revised: 8 July 2025 / Accepted: 17 July 2025 / Published: 19 July 2025
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications in Science and Engineering, 4th Edition)
Versions Notes

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 mean-square exponential input-to-state stability; mean-square exponential stability; almost sure exponential stability; Lyapunov functional; martingale convergence theorem

Share and Cite

MDPI and ACS Style

Xiao, H.; Xu, M.; Zhang, Y.; Weng, S. Stability of Stochastic Delayed Recurrent Neural Networks. Mathematics 2025, 13, 2310. https://doi.org/10.3390/math13142310

AMA Style

Xiao H, Xu M, Zhang Y, Weng S. Stability of Stochastic Delayed Recurrent Neural Networks. Mathematics. 2025; 13(14):2310. https://doi.org/10.3390/math13142310

Chicago/Turabian Style

Xiao, Hongying, Mingming Xu, Yuanyuan Zhang, and Shengquan Weng. 2025. "Stability of Stochastic Delayed Recurrent Neural Networks" Mathematics 13, no. 14: 2310. https://doi.org/10.3390/math13142310

APA Style

Xiao, H., Xu, M., Zhang, Y., & Weng, S. (2025). Stability of Stochastic Delayed Recurrent Neural Networks. Mathematics, 13(14), 2310. https://doi.org/10.3390/math13142310

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