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Quasi-projective Synchronization Control of Delayed Stochastic Quaternion-Valued Fuzzy Cellular Neural Networks with Mismatched Parameters

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Abstract

This paper deals with the quasi-projective synchronization problem of delayed stochastic quaternion fuzzy cellular neural networks with mismatch parameters. Although the parameter mismatch of the drive-response system increases the computational complexity of the article, it is of practical significance to consider the existence of deviations between the two systems. The method of this article is to design an appropriate controller and construct Lyapunov functional and stochastic analysis theory based on the Itô formula in the quaternion domain. We adopt the non-decomposable method of quaternion FCNN, which preserves the original data and reduces computational effort. We obtain sufficient conditions for quasi-projective synchronization of the considered random quaternion numerical FCNNs with mismatched parameters. Additionally, we estimate the error bounds of quasi-projective synchronization and then carry out a numerical example to verify their validity. Our results are novel even if the considered neural networks degenerate into real-valued or complex-valued neural networks. This article provides a good research idea for studying the quasi-projective synchronization problem of random quaternion numerical FCNN with time delay and has obtained good results. The method in this article can also be used to study the quasi-projective synchronization of a Clifford-valued neural network.

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Funding

This work is supported by the National Natural Sciences Foundation of the People’s Republic of China under Grant 11971421, the Yunnan Fundamental Research Projects under Grant 202201AU070170, the Science Research Fund Projects of Yunnan University of Finance and Economics under Grant 2023D40, and the Key Laboratory of Complex Dynamics System and Application Analysis of Department of Education of Yunnan Province.

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Authors and Affiliations

  1. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, 650221, China

    Xiaofang Meng, Yu Fei & Zhouhong Li

  2. Department of Mathematics, Yuxi Normal University, Yuxi, Yunnan, 653100, China

    Zhouhong Li

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  1. Xiaofang Meng
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  2. Yu Fei
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Correspondence to Zhouhong Li.

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Meng, X., Fei, Y. & Li, Z. Quasi-projective Synchronization Control of Delayed Stochastic Quaternion-Valued Fuzzy Cellular Neural Networks with Mismatched Parameters. Cogn Comput 16, 2206–2221 (2024). https://doi.org/10.1007/s12559-024-10299-9

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