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Asymptotically Almost Automorphic Solutions for Impulsive Quaternion-Valued Neural Networks with Mixed Delays

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Abstract

In this paper, we consider a class of impulsive quaternion-valued neural networks with mixed delays. By using the General Lipschitz condition, the contraction mapping principle, the exponential dichotomy of linear dynamic equations and the generalized Gronwall–Bellman inequality technique, we obtain the conditions for the existence, uniqueness and global exponential stability of asymptotically almost automorphic solutions of the system. Finally, two examples are given to illustrate the efficiency of our theoretical results.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 12071491) and by the Scientific Research Project of Guangdong Industry Polytechnic (Grant No. KJ2019-029).

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Authors and Affiliations

  1. Mathematics Teaching and Research Department, Guangdong Industry Polytechnic, No. 152, Xingang Xi Road, Guangzhou, 510300, Guangdong, People’s Republic of China

    Quande Jiang

  2. School of Mathematics, Sun Yat-sen University, No. 135, Xingang Xi Road, Guangzhou, 510275, Guangdong, People’s Republic of China

    Qiru Wang

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  1. Quande Jiang
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QJ: Writing-original draft. QW: Writing-review and editing.

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Correspondence to Quande Jiang.

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Jiang, Q., Wang, Q. Asymptotically Almost Automorphic Solutions for Impulsive Quaternion-Valued Neural Networks with Mixed Delays. Neural Process Lett 55, 12597–12624 (2023). https://doi.org/10.1007/s11063-023-11434-7

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