Exponential Stability Analysis of Mixed Delayed Quaternion-Valued Neural Networks Via Decomposed Approach
With the application of quaternion in technology, quaternion-valued neural networks (QVNNs) have attracted many scholars' attention in recent years. For the existing results, dynamical behavior is an important studying side. In this paper, we mainly research the existence, uniqueness and expone...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
IEEE
2020-01-01
|
Series: | IEEE Access |
Subjects: | |
Online Access: | https://ieeexplore.ieee.org/document/9093812/ |
id |
doaj-93b00ec05bb941828f6ef5bb6d7d5345 |
---|---|
record_format |
Article |
spelling |
doaj-93b00ec05bb941828f6ef5bb6d7d53452021-03-30T02:23:14ZengIEEEIEEE Access2169-35362020-01-018915019150910.1109/ACCESS.2020.29945549093812Exponential Stability Analysis of Mixed Delayed Quaternion-Valued Neural Networks Via Decomposed ApproachHuamin Wang0https://orcid.org/0000-0001-8180-8172Jie Tan1Shiping Wen2Department of Mathematics, Luoyang Normal University, Luoyang, ChinaCollege of Mathematics, Physics and Data Science, Chongqing University of Science and Technology, Chongqing, ChinaCentre for Artificial Intelligence, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW, AustraliaWith the application of quaternion in technology, quaternion-valued neural networks (QVNNs) have attracted many scholars' attention in recent years. For the existing results, dynamical behavior is an important studying side. In this paper, we mainly research the existence, uniqueness and exponential stability criteria of solutions for the QVNNs with discrete time-varying delays and distributed delays by means of generalized 2-norm. In order to avoid the noncommutativity of quaternion multiplication, the QVDNN system is firstly decomposed into four real-number systems by Hamilton rules. Then, we obtain the sufficient criteria for the existence, uniqueness and exponential stability of solutions by special Lyapunov-type functional, Cauchy convergence principle and monotone function. Furthermore, several corollaries are derived from the main results. Finally, we give one numerical example and its simulated figures to illustrate the effectiveness of the obtained conclusion.https://ieeexplore.ieee.org/document/9093812/Quaternion-valued neural networksdiscrete and distributed delaysexponential stabilitygeneralized 2-norm |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Huamin Wang Jie Tan Shiping Wen |
spellingShingle |
Huamin Wang Jie Tan Shiping Wen Exponential Stability Analysis of Mixed Delayed Quaternion-Valued Neural Networks Via Decomposed Approach IEEE Access Quaternion-valued neural networks discrete and distributed delays exponential stability generalized 2-norm |
author_facet |
Huamin Wang Jie Tan Shiping Wen |
author_sort |
Huamin Wang |
title |
Exponential Stability Analysis of Mixed Delayed Quaternion-Valued Neural Networks Via Decomposed Approach |
title_short |
Exponential Stability Analysis of Mixed Delayed Quaternion-Valued Neural Networks Via Decomposed Approach |
title_full |
Exponential Stability Analysis of Mixed Delayed Quaternion-Valued Neural Networks Via Decomposed Approach |
title_fullStr |
Exponential Stability Analysis of Mixed Delayed Quaternion-Valued Neural Networks Via Decomposed Approach |
title_full_unstemmed |
Exponential Stability Analysis of Mixed Delayed Quaternion-Valued Neural Networks Via Decomposed Approach |
title_sort |
exponential stability analysis of mixed delayed quaternion-valued neural networks via decomposed approach |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2020-01-01 |
description |
With the application of quaternion in technology, quaternion-valued neural networks (QVNNs) have attracted many scholars' attention in recent years. For the existing results, dynamical behavior is an important studying side. In this paper, we mainly research the existence, uniqueness and exponential stability criteria of solutions for the QVNNs with discrete time-varying delays and distributed delays by means of generalized 2-norm. In order to avoid the noncommutativity of quaternion multiplication, the QVDNN system is firstly decomposed into four real-number systems by Hamilton rules. Then, we obtain the sufficient criteria for the existence, uniqueness and exponential stability of solutions by special Lyapunov-type functional, Cauchy convergence principle and monotone function. Furthermore, several corollaries are derived from the main results. Finally, we give one numerical example and its simulated figures to illustrate the effectiveness of the obtained conclusion. |
topic |
Quaternion-valued neural networks discrete and distributed delays exponential stability generalized 2-norm |
url |
https://ieeexplore.ieee.org/document/9093812/ |
work_keys_str_mv |
AT huaminwang exponentialstabilityanalysisofmixeddelayedquaternionvaluedneuralnetworksviadecomposedapproach AT jietan exponentialstabilityanalysisofmixeddelayedquaternionvaluedneuralnetworksviadecomposedapproach AT shipingwen exponentialstabilityanalysisofmixeddelayedquaternionvaluedneuralnetworksviadecomposedapproach |
_version_ |
1724185311452332032 |