Finite-time synchronization for fractional-order delayed quaternion valued neural networks by using the negative definition of matrix

Zhimin Wan; Zhengqiu Zhang; Zhenbo Cheng; Zhimin Wan; Zhengqiu Zhang; Zhenbo Cheng

doi:10.3934/math.2026321

AIMS Mathematics

2026, Volume 11, Issue 3: 7791-7820. doi: 10.3934/math.2026321

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Research article

Finite-time synchronization for fractional-order delayed quaternion valued neural networks by using the negative definition of matrix

1.
Clinical Laboratory of Hunnan Provincial People' s Hospital, The First Hospital of Hunan Normal University, Changsha, 410000, China
2.
College of Mathematics, Hunan University, Changsha, 410006, China

Received: 06 December 2025 Revised: 02 March 2026 Accepted: 03 March 2026 Published: 24 March 2026
MSC : 34K24

In the study, the finite-time synchronization (FTSN) for a kind of master-slave quaternion-valued fractional-order neural networks (MSQVFONNS) is discussed. By using the negative definition of matrix and the properties of the determinant, two novel criteria on the FTSN for the considered MSFOQVNNS are established. The negative definition of the matrix and the properties of the determinant are introduced to study the FTSN for neural networks (NNs) in our article. Since until, studies about the FTSN for the NNs are rare and researchers have only used the linear matrix inequality (LMI), finite time stability theorems (FTSTs) of fractional order and Lyapunov direct method to study the FTSN for the MSFOQVNNS, so far, our method to study the FTSN for the MSFOQVNNS is of definite significance.
Citation: Zhimin Wan, Zhengqiu Zhang, Zhenbo Cheng. Finite-time synchronization for fractional-order delayed quaternion valued neural networks by using the negative definition of matrix[J]. AIMS Mathematics, 2026, 11(3): 7791-7820. doi: 10.3934/math.2026321

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Abstract

In the study, the finite-time synchronization (FTSN) for a kind of master-slave quaternion-valued fractional-order neural networks (MSQVFONNS) is discussed. By using the negative definition of matrix and the properties of the determinant, two novel criteria on the FTSN for the considered MSFOQVNNS are established. The negative definition of the matrix and the properties of the determinant are introduced to study the FTSN for neural networks (NNs) in our article. Since until, studies about the FTSN for the NNs are rare and researchers have only used the linear matrix inequality (LMI), finite time stability theorems (FTSTs) of fractional order and Lyapunov direct method to study the FTSN for the MSFOQVNNS, so far, our method to study the FTSN for the MSFOQVNNS is of definite significance.

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