Matrix measure-based exponential stability and synchronization of Markovian jumping QVNNs with time-varying delays and delayed impulses

Miao Zhang; Bole Li; Weiqiang Gong; Shuo Ma; Qiang Li; Miao Zhang; Bole Li; Weiqiang Gong; Shuo Ma; Qiang Li

doi:10.3934/math.20241618

AIMS Mathematics

2024, Volume 9, Issue 12: 33930-33955. doi: 10.3934/math.20241618

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Matrix measure-based exponential stability and synchronization of Markovian jumping QVNNs with time-varying delays and delayed impulses

1.
School of Information and Artificial Intelligence, Anhui Agricultural University, Hefei 230036, China
2.
School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, China
3.
School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China

Received: 05 November 2024 Revised: 20 November 2024 Accepted: 22 November 2024 Published: 02 December 2024
MSC : 00A69

This article explored the topics of global exponential stability and synchronization issues of a type of Markovian jumping quaternion-valued neural networks (QVNNs) that incorporate delayed impulses and time-varying delays. By utilizing the matrix measure strategy and delayed differential inequality techniques with an impulsive factor, several effective and practical criteria can be established to confirm that the impulsive QVNNs in question can achieve exponential synchronization with the given response system. Furthermore, the contained exponential convergence rate can be clearly presented. Notably, derived criteria are straightforward to verify and implement in real-world applications. In the end, to demonstrate the accuracy and effectiveness of achieved theoretical findings, one numerical example with an explanation was presented.
- quaternion-valued neural networks,
- Markovian jumping,
- synchronization,
- delayed impulses
Citation: Miao Zhang, Bole Li, Weiqiang Gong, Shuo Ma, Qiang Li. Matrix measure-based exponential stability and synchronization of Markovian jumping QVNNs with time-varying delays and delayed impulses[J]. AIMS Mathematics, 2024, 9(12): 33930-33955. doi: 10.3934/math.20241618

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Abstract

This article explored the topics of global exponential stability and synchronization issues of a type of Markovian jumping quaternion-valued neural networks (QVNNs) that incorporate delayed impulses and time-varying delays. By utilizing the matrix measure strategy and delayed differential inequality techniques with an impulsive factor, several effective and practical criteria can be established to confirm that the impulsive QVNNs in question can achieve exponential synchronization with the given response system. Furthermore, the contained exponential convergence rate can be clearly presented. Notably, derived criteria are straightforward to verify and implement in real-world applications. In the end, to demonstrate the accuracy and effectiveness of achieved theoretical findings, one numerical example with an explanation was presented.

References

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