Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays

Dong, Wenjun; Huang, Yujiao; Chen, Tingan; Fan, Xinggang; Long, Haixia

doi:10.3390/math10132157

Open AccessArticle

Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays

by

Wenjun Dong

¹,

Yujiao Huang

^1,*,

Tingan Chen

¹,

Xinggang Fan

¹

and

Haixia Long

²

¹

College of Zhijiang, Zhejiang University of Technology, Shaoxing 312030, China

²

College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310058, China

^*

Author to whom correspondence should be addressed.

Mathematics 2022, 10(13), 2157; https://doi.org/10.3390/math10132157

Submission received: 17 May 2022 / Revised: 9 June 2022 / Accepted: 17 June 2022 / Published: 21 June 2022

(This article belongs to the Special Issue Mathematic Control and Artificial Intelligence)

Download

Browse Figures

Versions Notes

Abstract

This study on the local stability of quaternion-valued neural networks is of great significance to the application of associative memory and pattern recognition. In the research, we study local Lagrange exponential stability of quaternion-valued neural networks with time delays. By separating the quaternion-valued neural networks into a real part and three imaginary parts, separating the quaternion field into

3^{4 n}

subregions, and using the intermediate value theorem, sufficient conditions are proposed to ensure quaternion-valued neural networks have

3^{4 n}

equilibrium points. According to the Halanay inequality, the conditions for the existence of

2^{4 n}

local Lagrange exponentially stable equilibria of quaternion-valued neural networks are established. The obtained stability results improve and extend the existing ones. Under the same conditions, quaternion-valued neural networks have more stable equilibrium points than complex-valued neural networks and real-valued neural networks. The validity of the theoretical results were verified by an example.

Keywords: quaternion-valued neural network; local Lagrange exponential stability; multiple equilibrium points; time delay

Share and Cite

MDPI and ACS Style

Dong, W.; Huang, Y.; Chen, T.; Fan, X.; Long, H. Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays. Mathematics 2022, 10, 2157. https://doi.org/10.3390/math10132157

AMA Style

Dong W, Huang Y, Chen T, Fan X, Long H. Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays. Mathematics. 2022; 10(13):2157. https://doi.org/10.3390/math10132157

Chicago/Turabian Style

Dong, Wenjun, Yujiao Huang, Tingan Chen, Xinggang Fan, and Haixia Long. 2022. "Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays" Mathematics 10, no. 13: 2157. https://doi.org/10.3390/math10132157

APA Style

Dong, W., Huang, Y., Chen, T., Fan, X., & Long, H. (2022). Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays. Mathematics, 10(13), 2157. https://doi.org/10.3390/math10132157

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

Local Lagrange Exponential Stability Analysis of Quaternion-Valued Neural Networks with Time Delays

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI