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Further Research on the Problems of Synchronization for Fractional-Order BAM Neural Networks in Octonion-Valued Domain

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Abstract

The problem of the globally asymptotical synchronization is studied for the system of fractional-order delayed octonion-valued BAM neural networks (FODOVBAMNNs) and the problem of the global Mittag–Leffler synchronization is researched for the system of fractional-order octonion-valued BAM neural networks (FOVBAMNNs), respectively. First, the new octonion-valued models are established for investigated systems with linear threshold activation functions which can be useful for the reduction in computation. Then, because of neither commutativity nor associativity of octonion multiplication, the novel systems of FODOVBAMNNs and FOVBAMNNs are separated into four dimensionality reduction systems which can be called fractional-order delayed complex-valued BAM neural networks (FODCVBAMNNs) and fractional-order complex-valued BAM neural networks (FCVBAMNNs) owe to the application of Cayley–Dichson approach. In addition, the further criteria are acquired for the problems of the globally asymptotical synchronization and the global Mittag–Leffler synchronization for FODOVBAMNNs and FOVBAMNNs by the feature of Caputo fractional derivative, methods for dynamic analysis of delayed neural networks, interactive character of BAM, the novel LKFs, the very recent inequalities containing some parameters and the new design for the linear feedback controllers including sign function and so on. Finally, two simulation examples are demonstrated to express the feasibility and improvement of the obtained results.

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Acknowledgements

This work was supported in part by National Natural Science Foundation of China under grant 12001452 and also in part by the Chunhui Plan cooperative scientific research project of Ministry of Education of China under grant HZKY20220580 and also in part by the Program of Science and Technology of Sichuan Province of China under grant 2021ZYD0012, 2022NSFSC0532 and in part by Open Fund (PLN2022-20) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, China (Southwest Petroleum University).

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Authors and Affiliations

  1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610050, China

    Jianying Xiao & Xiao Guo

  2. School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu, 610106, China

    Jianying Xiao

  3. College of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu, 610050, China

    Yongtao Li

  4. Centre for Artificial Intelligence, Faculty of Engineering Information Technology, University of Technology Sydney, Ultimo, NSW, 2007, Australia

    Shiping Wen

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Xiao, J., Guo, X., Li, Y. et al. Further Research on the Problems of Synchronization for Fractional-Order BAM Neural Networks in Octonion-Valued Domain. Neural Process Lett 55, 11173–11208 (2023). https://doi.org/10.1007/s11063-023-11371-5

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