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New exploration on bifurcation for fractional-order quaternion-valued neural networks involving leakage delays

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Abstract

During the past decades, many works on Hopf bifurcation of fractional-order neural networks are mainly concerned with real-valued and complex-valued cases. However, few publications involve the quaternion-valued neural networks which is a generalization of real-valued and complex-valued neural networks. In this present study, we explorate the Hopf bifurcation problem for fractional-order quaternion-valued neural networks involving leakage delays. Taking advantage of the Hamilton rule of quaternion algebra, we decompose the addressed fractional-order quaternion-valued delayed neural networks into the equivalent eight real valued networks. Then the delay-inspired bifurcation condition of the eight real valued networks are derived by making use of the stability criterion and bifurcation theory of fractional-order differential dynamical systems. The impact of leakage delay on the bifurcation behavior of the involved fractional-order quaternion-valued delayed neural networks has been revealed. Software simulations are implemented to support the effectiveness of the derived fruits of this study. The research supplements the work of Huang et al. (Neural Netw 117:67–93, 2019).

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Acknowledgements

This work is supported by National Natural Science Foundation of China (No. 62062018), Guizhou Key Laboratory of Big Data Statistical Analysis (No. [2019]5103), and Project of High-level Innovative Talents of Guizhou Province ([2016]5651), Key Project of Hunan Education Department (17A181), University Science and Technology Top Talents Project of Guizhou Province (KY[2018]047), Foundation of Science and Technology of Guizhou Province ([2019]1051), Guizhou University of Finance and Economics(2018XZD01).

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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. Guizhou Key Laboratory of Big Data Statistical Analysis, Guiyang, 550025, People’s Republic of China

    Changjin Xu

  3. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550004, People’s Republic of China

    Zixin Liu

  4. Faculty of Sciences of Bizerta, UR13ES47 Research Units of Mathematics and Applications, University of Carthage, Bizerta, 7021, Tunisia

    Chaouki Aouiti

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

    Peiluan Li & Jinling Yan

  6. Library, Guizhou University of Finance and Economics, Guiyang, 550004, People’s Republic of China

    Lingyun Yao

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  1. Changjin Xu
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Correspondence to Changjin Xu.

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Xu, C., Liu, Z., Aouiti, C. et al. New exploration on bifurcation for fractional-order quaternion-valued neural networks involving leakage delays. Cogn Neurodyn 16, 1233–1248 (2022). https://doi.org/10.1007/s11571-021-09763-1

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