Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances

Jibin Yang, Xiaohui Xu (), Quan Xu, Haolin Yang and Mengge Yu
Additional contact information
Jibin Yang: Vehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Xihua University, Chengdu 610039, China
Xiaohui Xu: Vehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Xihua University, Chengdu 610039, China
Quan Xu: School of Mechanical Engineering, Xihua University, Chengdu 610039, China
Haolin Yang: Vehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Xihua University, Chengdu 610039, China
Mengge Yu: College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China

Mathematics, 2024, vol. 12, issue 6, 1-26

Abstract: This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method, some criteria are provided for securing the mean-square exponential stability of the mixed-delay QVNNs under impulsive and stochastic disturbances. Furthermore, a type of chaotic QVNNs under stochastic and impulsive disturbances is considered using a previously established stability analysis method. After the completion of designing the linear feedback control law, some sufficient conditions are obtained using the vector Lyapunov function method for determining the mean-square exponential synchronization of drive–response systems. Finally, two examples are provided to demonstrate the correctness and feasibility of the main findings and one example is provided to validate the use of QVNNs for image associative memory.

Keywords: quaternion-valued neural networks; impulsive disturbances; stochastic disturbances; mixed delays; mean-square exponential stability; mean-square exponential synchronization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/6/917/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/6/917/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:6:p:917-:d:1360550

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().