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Bifurcation investigation and control scheme of fractional neural networks owning multiple delays

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Abstract

In this current study, novel fractional neural networks owning delay are formulated. Using Lipschitz condition, we demonstrate that the solution of the formulated fractional delayed neural networks exists and is unique. Applying a reasonable function, we handle the boundedness issue of solution to the formulated fractional delayed neural networks. Exploiting the stability criterion and bifurcation viewpoint of the fractional order delayed dynamical system, we explore the stability and bifurcation phenomenon of the established fractional delayed neural networks. Taking advantage of an adequate hybrid controller, we have efficaciously dominated the stability domain and the time of generation of bifurcation of the formulated fractional delayed neural networks. Ultimately, computer simulation graphs are provided to sustain our acquired outcomes. The acquired theoretical outcomes of this study possess considerable realistic meaning in regulating and controlling neural networks.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Nos. 12261015, 62062018), Project of High-level Innovative Talents of Guizhou Province ([2016]5651), Guizhou Key Laboratory of Big Data Statistical Analysis (No. [2019]5103), University Science and Technology Top Talents Project of Guizhou Province (KY [2018]047) and Theoretical, Empirical, and Policy Research on Psychological Capital Assisting Guizhou Peasants in Increasing Income and Becoming Rich (21GZZD08).

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Authors and Affiliations

  1. Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, 550004, People’s Republic of China

    Changjin Xu

  2. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550025, People’s Republic of China

    Yingyan Zhao, Jinting Lin, Yicheng Pang & Zixin Liu

  3. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, 450046, People’s Republic of China

    Jianwei Shen

  4. School of Mathematics and Physics, University of South China, Hengyang, 421001, People’s Republic of China

    Maoxin Liao

  5. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, People’s Republic of China

    Peiluan Li

  6. School of Information Science and Technology, Fudan University, Shanghai, 200433, People’s Republic of China

    Youxiang Qin

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  1. Changjin Xu
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  2. Yingyan Zhao
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Xu, C., Zhao, Y., Lin, J. et al. Bifurcation investigation and control scheme of fractional neural networks owning multiple delays. Comp. Appl. Math. 43, 186 (2024). https://doi.org/10.1007/s40314-024-02718-2

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