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Almost Anti-periodic Solution of Inertial Neural Networks with Leakage and Time-Varying Delays on Timescales

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Abstract

This paper studies a class of inertial neural networks with leakages and varying delays on timescales:

$$\begin{aligned} x_{i}^{\bigtriangleup \bigtriangleup }(t)&=-a_{i}(t)x_{i}^{\bigtriangleup }(t-\eta _{i} (t))- b_{i}(t)x_{i}(t-\xi _{i} (t)) +\sum \limits _{j=1}^{n} c_{ij}(t)f_{j}(x_{j}(t))\\&\quad +\sum \limits _{j=1}^{n} d_{ij}(t)g_{j}(x_{j}(t- q_{ij}(t)))+S_{i}(t). \end{aligned}$$

The problems of the existence, the uniqueness and the exponential stability of almost anti-periodic solution on timescales are investigated. We establish some sufficient conditions to guarantee the main results, by constructing the Lyapunov functions and using some classical inequalities. A numerical example is given for illustration.

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Acknowledgements

We would like to thank both anonymous reviewers and the editor for their insightful comments on the paper, as these comments led us to an improvement of the work.

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Authors and Affiliations

  1. Laboratory of Engineering Mathematics (LR01ES13), Tunisia Polytechnic School, University of Carthage, Tunis, Tunisia

    Adnène Arbi, Najeh Tahri & Chaker Jammazi

  2. National School of Advanced Sciences and Technologies of Borj Cedria, University of Carthage, Tunis, Tunisia

    Adnène Arbi

  3. National Engineering School of Tunis, University of Tunis El Manar, Tunis, Tunisia

    Chaker Jammazi

  4. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, China

    Chuangxia Huang

  5. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha, Hunan, 410114, China

    Chuangxia Huang

  6. Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and School of Mathematics, Southeast University, Nanjing, China

    Jinde Cao

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  1. Adnène Arbi
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  2. Najeh Tahri
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  4. Chuangxia Huang
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  5. Jinde Cao
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Correspondence to Adnène Arbi.

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Arbi, A., Tahri, N., Jammazi, C. et al. Almost Anti-periodic Solution of Inertial Neural Networks with Leakage and Time-Varying Delays on Timescales. Circuits Syst Signal Process 41, 1940–1956 (2022). https://doi.org/10.1007/s00034-021-01894-4

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  • DOI: https://doi.org/10.1007/s00034-021-01894-4

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