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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (6): 1041-1052.doi: 10.3969/j.issn.1005-3085.2024.06.004

• • 上一篇    下一篇

变时滞四元数值Cohen-Grossberg神经网络全局$\mu$稳定性分析

杨艳平,  陈展衡   

  1. 伊犁师范大学数学与统计学院，伊宁 835000
  • 收稿日期:2022-04-07 接受日期:2022-11-12 出版日期:2024-12-15 发布日期:2024-12-15
  • 通讯作者: 陈展衡 E-mail: czh918czh@163.com
  • 基金资助:
    新疆维吾尔自治区自然科学基金 (2024D01C196).

Global $\mu$-stability Analysis of Quaternion-valued Cohen-Grossberg Neural Networks with Time-varying Delays

YANG Yanping,  CHEN Zhanheng   

  1. School of Mathematics and Statistics, Yili Normal University, Yining 835000
  • Received:2022-04-07 Accepted:2022-11-12 Online:2024-12-15 Published:2024-12-15
  • Contact: Z. Chen. E-mail address: czh918czh@163.com
  • Supported by:
    The Natural Science Foundation of Xinjiang Uygu Autonomous Region (2024D01C196).

摘要：

研究了具有变时滞的四元数值Cohen-Grossberg神经网络的全局$\mu$稳定性。首先，将变时滞概念引入神经网络模型，从而构建了一个能更精确反映神经元动态特性的模型。接着，通过应用同胚映射定理，探讨了平衡点存在的唯一性，并确定了系统存在唯一平衡点的充分条件。鉴于四元数乘法的非交换特性，研究将四元数值神经网络系统分解为四个等价的实值神经网络系统。在此基础上，通过构造合适的Lyapunov函数，得到了系统全局$\mu$稳定的充分条件。最终，通过数值仿真实验，验证了该系统的全局$\mu$稳定性，从而证实了理论结论的有效性和准确性。

关键词: 四元数, $\mu$稳定, Cohen-Grossberg神经网络, Lyapunov函数

Abstract:

This research investigates the global $\mu$-stability of a quaternion-valued Cohen-Grossberg neural network with time-varying delays. The study first introduces the concept of time-varying delays into the neural network model, thereby constructing a more precise model that reflects the dynamic characteristics of neurons. Subsequently, by applying the theorem of homeomorphism, the uniqueness of equilibrium points is discussed, and the sufficient conditions for the existence of a unique equilibrium point in the system are determined. In view of the non-commutativity property of quaternion multiplication, the quaternion-valued neural network system is decomposed into four equivalent real-valued neural network systems. On this basis, by constructing an appropriate Lyapunov function, the sufficient conditions for the global $\mu$-stability of the system are obtained. Finally, through numerical simulation experiments, the global $\mu$-stability of the system is verified, thereby confirming the effectiveness and accuracy of the theoretical conclusions.

Key words: quaternion-valued, $\mu$-stability, Cohen-Grossberg neural network, Lyapunov function

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