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Stability Analysis of Quaternion-Valued Neutral Neural Networks with Generalized Activation Functions

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Abstract

Stability is a central issue in the study of dynamical systems, and quaternion-valued neural networks (QVNNs) perform well in handling the problem involving high-dimension date. The paper is dedicated to investigating the stability problem of QVNNs with neutral delay. In order to accurately estimate the derivative of Lyapunov functional, both reciprocally convex inequality and Wirtinger-based inequality are extended to the quaternion domain. And the direct quaternion method is used to analyze the quaternion-valued neutral neural networks (QVNNNs). Based on the generalized inequalities, the existence, uniqueness, and global stability criteria for QVNNS with several freedom matrices are derived. Concision and compact stability criteria of QVNNNs are established in the form of quaternion-valued LMIs, and the correctness of the theoretical results was verified through a numerical example.

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Funding

This work was jointly supported by the National Natural Science Foundation of China under Grant No. 11601047, the Natural Science Foundation Project of Chongqing under grant Nos. cstc2021jcyj-msxmX0051, cstc2021jcyj-msxm2025, the Science and Technology Innovation Project of Economic Circle Construction in Chengdu-Chongqing Area under Grant No. KJCX2020047, the Science and Technology Research Program of Chongqing Municipal Education Commission under grant Nos. KJZD-K202201202, KJQN202101228, KJQN202101220, KJZD-M202001201.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China

    Yanqiu Wu, Zhengwen Tu, Liangwei Wang & Tao Peng

  2. School of Electronic and Information Engineering, Chongqing Three Gorges University, Wanzhou, 404100, China

    Nina Dai

  3. Experiment and Practice Centre, Chongqing Three Gorges University, Wanzhou, 404100, China

    Ning Hu

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  1. Yanqiu Wu
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  3. Nina Dai
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Correspondence to Zhengwen Tu.

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Wu, Y., Tu, Z., Dai, N. et al. Stability Analysis of Quaternion-Valued Neutral Neural Networks with Generalized Activation Functions. Cogn Comput 16, 392–403 (2024). https://doi.org/10.1007/s12559-023-10212-w

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  • DOI: https://doi.org/10.1007/s12559-023-10212-w

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