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Quasi-Synchronization for Fractional-Order Reaction–Diffusion Quaternion-Valued Neural Networks: An LMI Approach

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Abstract

In this paper, we study the quasi-synchronization control for a class of fractional-order quaternion-valued neural networks (QVNNs). Unlike previous studies, the introduce of the reaction–diffusion terms makes the model more comprehensive. It is worth mentioning that in earlier literature, there are rare results based on linear matrix inequality method when using the decomposition method (dividing the system into four real-valued ones) to study the synchronization for QVNNs, which is due to the great challenge posed by the cross-product terms. In this work, we overcome this problem by processing the cross-product term as some free variables and then obtain the quasi-synchronization criterion of the system by linear matrix inequalities (LMI) method, which extends some previous works. Finally, a numerical example is given to support the results of this paper.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 61976081 and 62203153, in part by the Natural Science Fund for Excellent Young Scholars of Henan Province under Grant 202300410127, in part by Key Scientific Research Projects of Higher Education Institutions in Henan Province under Grant 22A413001, in part by Top Young Talents in Central Plains under Grant Yuzutong (2021)44, in part by Technology Innovative Teams in University of Henan Province under Grant 23IRTSTHN012, and in part by the Natural Science Fund for Young Scholars of Henan Province under Grant 222300420151.

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Correspondence to Xiaona Song.

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Sun, X., Song, X., Man, J. et al. Quasi-Synchronization for Fractional-Order Reaction–Diffusion Quaternion-Valued Neural Networks: An LMI Approach. Neural Process Lett 55, 4499–4517 (2023). https://doi.org/10.1007/s11063-022-11054-7

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