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Concise Exponential Stability Conditions for BAM Quaternion Memristive Neural Networks Affected by Mixed Delays

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Abstract

The concise exponential stability conditions for bidirectional associative memory (BAM) quaternion memristive neural networks affected by mixed delays are presented. The involved delays include multiple time-varying transmission delays and unbounded distribution delays. To show global exponential stability conditions, a new method built on the estimation of solutions is presented. The acquired stability conditions consist of several scalar inequalities, which are concise and can be easily solved. A numerical example is offered to demonstrate the applicability of the theoretical results. Notably, after a minor modification, the method built on the estimation of solutions is found to be applicable for many delayed system models.

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Grant No. 12,401,343), the Heilongjiang Provincial Natural Science Foundation of China (Grant No. YQ2021F014), Basic Research Foundation for Outstanding Young Teachers at Heilongjiang Provincial Universities of China (Grant No. YQJH2023141), and Fundamental Research Funds in Heilongjiang Provincial Universities of China (Grant No. 2022-KYYWF-1099).

The authors would like to thank the anonymous associate editor and reviewers for their helpful comments and suggestions, which greatly improved the original version of the paper.

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Authors and Affiliations

  1. College of Science, Heilongjiang Institute of Technology, Harbin, 150050, China

    Zhiwei Zhang

  2. School of Mathematical Science, Heilongjiang University, Harbin, 150080, China

    Xiaona Yang & Xian Zhang

  3. Primary School Affiliated with Harbin Normal University, Harbin, 150086, China

    Hongwei Guan

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Correspondence to Xiaona Yang or Xian Zhang.

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Zhang, Z., Yang, X., Guan, H. et al. Concise Exponential Stability Conditions for BAM Quaternion Memristive Neural Networks Affected by Mixed Delays. Circuits Syst Signal Process 44, 128–140 (2025). https://doi.org/10.1007/s00034-024-02856-2

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