时滞可交换四元数神经网络稳定性分析

doi:10.11959/j.issn.2096-6652.202009

智能科学与技术学报 ›› 2020, Vol. 2 ›› Issue (1): 80-87.doi: 10.11959/j.issn.2096-6652.202009

时滞可交换四元数神经网络稳定性分析

林东源¹,陈晓丰¹,孙文涛²(),李伟凯³,夏砚楠¹

¹ 重庆交通大学数学与统计学院，重庆 400074
² 西藏大学理学院，西藏拉萨 850000
³ 南京航空航天大学计算机科学与技术学院，江苏南京 210016

修回日期:2020-02-19 出版日期:2020-03-20 发布日期:2020-04-10
作者简介:林东源（1996- ），男，重庆交通大学数学与统计学院硕士生，主要研究方向为四元数神经网络的动力学行为|陈晓丰（1980- ），男，博士，重庆交通大学数学与统计学院副教授、硕士生导师，主要研究方向为复数及四元数神经网络稳定性理论|孙文涛（1979- ），男，西藏大学理学院讲师，主要研究方向为四元数神经网络稳定性理论及应用|李伟凯（1994- ），男，南京航空航天大学计算机科学与技术学院博士生，主要研究方向为机器学习、迁移学习、领域适配|夏砚楠（1997- ），男，重庆交通大学数学与统计学院硕士生，主要研究方向为分数阶四元数神经网络的动力学行为
基金资助:
重庆市自然科学基金资助项目(cstc2017jcyjAX0082);重庆市自然科学基金资助项目(cstc2018jcyjAX0606);重庆市教育委员会科学技术研究基金资助项目(KJQN201900701)

Stability analysis of commutative quaternion valued neural network with time varying delays

Dongyuan LIN¹,Xiaofeng CHEN¹,Wentao SUN²(),Weikai LI³,Yannan XIA¹

¹ College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China
² School of Science,Tibet University,Lhasa 850000,China
³ College of Computer Science ＆Technology,Nanjing University of Aeronautics ＆Astronautics,Nanjing 210016,China

Revised:2020-02-19 Online:2020-03-20 Published:2020-04-10
Supported by:
Natural Science Foundation of Chongqing(cstc2017jcyjAX0082);Natural Science Foundation of Chongqing(cstc2018jcyjAX0606);Scientific and Technology Research Program of Chongqing Municipal Education Commission(KJQN201900701)

摘要/Abstract

摘要：

针对传统的四元数乘法运算不满足交换律的问题，介绍了一种可交换四元数，同时建立一种交换四元数神经网络（CQVNN），并对CQVNN的渐近稳定性进行研究。研究过程中，将CQVNN分解成4个实值神经网络，通过拓扑度理论、传统的李雅普诺夫稳定性理论以及不等式理论，得到CQVNN平衡点的存在唯一性条件以及其平衡点渐近稳定的充分条件。最后，给出一个数值案例，以验证所得结论的有效性。

关键词: 交换四元数, 时滞神经网络, 渐近稳定性

Abstract:

Because the traditional quaternion multiplication does not meet the commutative law,a kind of commutative quaternion was introduced,and a commutative quaternion valued neural network (CQVNN) was established,and the asymptotic stability of the CQVNN was studied.In the course of research,the CQVNN were decomposed into four real-valued neural networks.Then,through the topological degree theory,the traditional Lyapunov stability theory and the inequality theory,the conditions for the existence and uniqueness of the equilibrium point of CQVNN and the linear matrix inequality (LMI) conditions for the asymptotically stable of equilibrium point were obtained.Finally,a numerical example was given to verify the validity of the conclusion.

Key words: commutative quaternion, delayed neural network, asymptotically stability

中图分类号:

O175.13

林东源, 陈晓丰, 孙文涛, 等. 时滞可交换四元数神经网络稳定性分析[J]. 智能科学与技术学报, 2020, 2(1): 80-87.

Dongyuan LIN, Xiaofeng CHEN, Wentao SUN, et al. Stability analysis of commutative quaternion valued neural network with time varying delays[J]. Chinese Journal of Intelligent Science and Technology, 2020, 2(1): 80-87.

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时滞可交换四元数神经网络稳定性分析

Stability analysis of commutative quaternion valued neural network with time varying delays

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