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《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (2): 43-49.doi: 10.6040/j.issn.1671-9352.0.2024.352

• • 上一篇    

具有3个时滞的递归神经网络系统的稳定性分析

陈子杰,赵东霞*,王一言   

  1. 中北大学数学学院, 山西 太原 030051
  • 发布日期:2026-02-13
  • 通讯作者: 赵东霞(1981— ),女,副教授,硕士生导师,博士,研究方向为微分方程稳定性理论. E-mail:zhaodongxia6@sina.com
  • 作者简介:陈子杰(2001— ),男,硕士研究生,研究方向为微分方程稳定性理论. E-mail:2953110260@qq.com*通信作者:赵东霞(1981— ),女,副教授,硕士生导师,博士,研究方向为微分方程稳定性理论. E-mail:zhaodongxia6@sina.com
  • 基金资助:
    山西省基础研究计划资助项目(202403021221124)

Stability analysis of recurrent neural network systems with three delays

CHEN Zijie, ZHAO Dongxia*, WANG Yiyan   

  1. School of Mathematics, North University of China, Taiyuan 030051, Shanxi, China
  • Published:2026-02-13

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摘要： 研究由3个神经元组成的具有3个时滞的递归神经网络模型的稳定性。首先对系统在平衡点附近进行线性化处理, 求得其特征方程为含有两个指数项的超越方程。其次利用指数型多项式零点分布定理和特征根分析方法, 讨论系统稳定性切换的临界条件。最后建立保证系统稳定时参数需满足的充分性条件, 并给出3个时滞参数的临界取值。

关键词: 递归神经网络, 多时滞, 特征根分析方法, 稳定性

Abstract: The paper investigates the stability of a recursive neural network model composed of three neurons with three delays. Initially, the system is linearized around its equilibrium point, and the characteristic equation, which contains two exponential terms, is derived. Subsequently, the critical conditions for stability switch are discussed by zero-point distribution properties of exponential polynomials and methods of eigenvalue analysis. Finally, the sufficient conditions are given to ensure the system stable, and the critical values of time-delay are deduced.

Key words: recursive neural network, multiple time delays, eigenvalue analysis, stability

中图分类号: 

  • O175
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