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Asymptotic Stability of Fractional-Order Incommensurate Neural Networks

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Abstract

The dynamics and stability of fractional-order (FO) neural networks (FONN) and FO memristive neural networks (FOMNN), have received great attention in the last years. However, most research focused merely on commensurate FONN (all neurons have the same order). This paper addresses the stability of a class of incommensurate FONN for the first time. Firstly, using the comparison principle for FO systems with multi-order, the stability of FO nonlinear systems with multi-order is treated similarly to the stability of incommensurate FO linear systems. Then, adopting the stability results of incommensurate FO linear systems, an asymptotic stability criterion for FONN is established. The proposed method is valid for investigating the stability and synchronization of uncertain FONN and FOMNN with multi-order. Numerical simulations illustrate the theoretical results and their effectiveness.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 62073114; 11971032), Fundamental Research Funds for the Central Universities (Nos. JZ2021HGTA0146; JZ2021HGQA0193).

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, 230009, China

    Liping Chen, Panpan Gu, Shuiqing Xu & Suoliang Ge

  2. LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    António M. Lopes

  3. School of Automation, Chongqing University, Chongqing, 400044, China

    Yi Chai

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  1. Liping Chen
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  2. Panpan Gu
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  3. António M. Lopes
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Correspondence to Panpan Gu.

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Chen, L., Gu, P., Lopes, A.M. et al. Asymptotic Stability of Fractional-Order Incommensurate Neural Networks. Neural Process Lett 55, 5499–5513 (2023). https://doi.org/10.1007/s11063-022-11095-y

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