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Global Exponential Stability of High-Order Bidirectional Associative Memory (BAM) Neural Networks with Proportional Delays

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Abstract

This paper considers the global exponential stability (GES) of high-order bidirectional associative memory (BAM) neural networks with proportional delays. Here, proportional delays are unbounded time-varying delays, which are different from constant delays, bounded time-varying delays and distributed delays. Through variable transformations, the original system can be transformed equivalently into high-order BAM neural networks with multi-constant delays and time-varying coefficients. By utilizing Brouwer’s fixed point theorem and constructing appropriate delay differential inequalities, new sufficient criteria are established to guarantee the existence, uniqueness and GES of the equilibrium point for the considered model. Finally, two examples with numerical simulations are presented to demonstrate the effectiveness of the proposed results.

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Acknowledgements

The research of Z. X. Yu was partially supported by Natural Science Foundation of Shanghai (No. 18ZR1426500). The authors thank the referees and the Editor-in-Chief for their valuable comments and suggestions that help the improvement of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Jiacheng Zu & Zhixian Yu

  2. Department of Mathematics, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Jiacheng Zu

  3. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Yanling Meng

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  1. Jiacheng Zu
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  2. Zhixian Yu
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  3. Yanling Meng
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Correspondence to Zhixian Yu.

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Zu, J., Yu, Z. & Meng, Y. Global Exponential Stability of High-Order Bidirectional Associative Memory (BAM) Neural Networks with Proportional Delays. Neural Process Lett 51, 2531–2549 (2020). https://doi.org/10.1007/s11063-020-10206-x

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