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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (8): 103-110.doi: 10.6040/j.issn.1671-9352.0.2021.618

• • 上一篇    

具有多时滞和多参数的双向环状网络的稳定性

庞玉婷,赵东霞*,鲍芳霞   

  1. 中北大学理学院, 山西 太原 030051
  • 出版日期:2022-08-20 发布日期:2022-06-29
  • 作者简介:庞玉婷(1997— ), 女, 硕士研究生, 研究方向为微分方程稳定性理论. E-mail:2116786325@qq.com*通信作者简介:赵东霞(1981— ), 女, 博士, 副教授, 硕士生导师, 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(20210302123046)

Stability of the bidirectional ring networks with multiple time delays and multiple parameters

PANG Yu-ting, ZHAO Dong-xia*, BAO Fang-xia   

  1. School of Science, North University of China, Taiyuan 030051, Shanxi, China
  • Online:2022-08-20 Published:2022-06-29

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摘要： 针对具有多时滞和多参数的四元双向环形神经网络系统进行动力学分析,首先在平凡解附近对系统进行线性化处理,得到系统的特征方程。然后对特征方程进行因式分解,将其分解为四个一阶指数型多项式的连乘。进而,利用指数型多项式零点分布性质,建立系统与时滞相关及与时滞无关的稳定性充分条件。此外,将所得结论与已有文献中的结果做了详尽的对比分析,并利用数值模拟佐证了理论分析的有效性和优越性。

关键词: 双向环形神经网络, 多时滞, 指数型多项式, 稳定性

Abstract: The dynamic analysis of the four-neuron ring neural network with multiple time delays and multiple parameters is carried out. Firstly, the system is linearized near the trivial solution, and the characteristic equation of the system is obtained. Then the characteristic equation is factorized into four first-order exponential polynomials. Furthermore, by using the zero-point distribution property of exponential polynomial, sufficient conditions for the delay-dependent and delay-independent stability are established. Moreover, an exhaustive comparison analysis is made between the results obtained and those in the existing literature. Finally, some numerical simulations are presented to show the effectiveness and superiority of the results.

Key words: bidirectional ring neural network, multiple time delays, exponential polynomial, stability

中图分类号: 

  • O175.13
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