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Bifurcation Study for Fractional-Order Three-Layer Neural Networks Involving Four Time Delays

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Abstract

During the past several decades, many scholars deal with the stability behavior and Hopf bifurcation phenomenon of fractional-order delayed neural networks. However, the literature involving the stability issue and Hopf bifurcation behavior of fractional-order neural networks with multiple time delays is relatively scarce. This article is principally concerned with the stability problem and of Hopf bifurcation behavior of fractional-order three-layer neural networks involving multiple time delays. Variable substitution, Laplace transform, bifurcation principle of fractional-order dynamical system and computer simulation skill are employed. The delay-independent stability criterion and the sufficient condition of onset of Hopf bifurcation of three-layer neural networks are set up. It shows that if the sum of both different delays passes a key value, then the system loses its stability and the Hopf bifurcation phenomenon will take place. The study manifests that delay plays a most momentous part in stabilizing system and controlling bifurcation behavior for the fractional-order delayed three-layer neural networks. The researchful results of this article are an important theoretical cornerstone in controlling and adjusting neural networks. The obtained conclusions are completely novel and complement the earlier research results.

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Funding

The work is supported by National Natural Science Foundation of China (No.61673008 and No.62062018) and Project of High-level Innovative Talents of Guizhou Province ([2016]5651) and Major Research Project of The Innovation Group of The Education Department of Guizhou Province ([2017]039), Key Project of Hunan Education Department (17A181), Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (Changsha University of Science & Technology)(2018MMAEZD21), University Science and Technology Top Talents Project of Guizhou Province (KY[2018]047), Guizhou University of Finance and Economics (2018XZD01) and Foundation of Science and Technology of Guizhou Province ([2019]1051).

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Authors and Affiliations

  1. Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, 550004, PR China

    Changjin Xu

  2. College of Economics and Statistics, Guangzhou University, Guangzhou, 510006, PR China

    Wei Zhang

  3. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550004, PR China

    Zixin Liu

  4. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, PR China

    Peiluan Li

  5. Library, Guizhou University of Finance and Economics, Guiyang, 550004, PR China

    Lingyun Yao

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  1. Changjin Xu
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Correspondence to Wei Zhang.

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Xu, C., Zhang, W., Liu, Z. et al. Bifurcation Study for Fractional-Order Three-Layer Neural Networks Involving Four Time Delays. Cogn Comput 14, 714–732 (2022). https://doi.org/10.1007/s12559-021-09939-1

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