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Insight into Hopf Bifurcation and Control Methods in Fractional Order BAM Neural Networks Incorporating Symmetric Structure and Delay

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Abstract

The trait of solution, bifurcation mechanism, and stability of delayed BAM neural network models have attracted great attention from many scholars. But the exploration about the stability aspect and bifurcation mechanism of fractional delayed BAM neural network models is relatively few. This work will focus on the stability aspect and bifurcation mechanism of fractional delayed BAM neural network models. Lipschitz condition, Laplace transform, construction of a proper function, stability criterion, and bifurcation principle of fractional delayed dynamical system, delayed feedback controller, dislocated feedback controller, and Matlab simulation technique are exploited. The criteria on the boundedness, existence, and uniqueness of solutions to fractional delayed BAM neural network models are gained. A new delay-independent bifurcation criterion and stability of the formulated neural network models is acquired. Delayed feedback controller and dislocated feedback controller are effectually utilized to dominate the time of generation of bifurcation and stability domain of the formulated neural network models. MATLAB simulation experiments are provided to substantiate the acquired primary outcomes. The gained theoretical outcomes of this article possess tremendous theoretical significance in devising and running the fractional delayed BAM neural network models.

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Data Availability

No data were used to support this study.

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Funding

This work is supported by the National Natural Science Foundation of China (No.12261015, No.62062018), Project of High-level Innovative Talents of Guizhou Province ([2016]5651), Guizhou Key Laboratory of Big Data Statistical Analysis (No.[2019]5103), 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), and Guizhou University of Finance and Economics (2018XZD01).

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Authors and Affiliations

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

    Peiluan Li, Yuejing Lu & Jing Ren

  2. Longmen Laboratory, Henan, 471003, Luoyang, People’s Republic of China

    Peiluan Li, Yuejing Lu & Jing Ren

  3. Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, 550025, Guiyang, People’s Republic of China

    Changjin Xu

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  1. Peiluan Li
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Correspondence to Changjin Xu.

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Li, P., Lu, Y., Xu, C. et al. Insight into Hopf Bifurcation and Control Methods in Fractional Order BAM Neural Networks Incorporating Symmetric Structure and Delay. Cogn Comput 15, 1825–1867 (2023). https://doi.org/10.1007/s12559-023-10155-2

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