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Convergence analysis on time scales for HOBAM neural networks in the Stepanov-like weighted pseudo almost automorphic space

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Abstract

We start by presenting the concept of Stepanov-like weighted pseudo almost automorphic on time-space scales. Besides, we introduce a novel model of high-order BAM neural networks with mixed delays. To the best of our knowledge, this is the first time to study the convergence analysis for one system modeling the recurrent neural networks. Since it is a \(\Delta \)-dynamic system on time-space scales, the results obtained in our work are new and attractive. The main difficulty in our theoretical work is the construction of Lyapunov–Krasovskii functional and the application of the Banach’s fixed-point theorem. By fabricating an appropriate Lyapunov–Krasovskii Functional (LKF), some new sufficient conditions are obtained in terms of linear algebraic equations to guarantee the convergence to the Stepanov-like WPAA on time-space scales solution for the labeled neural networks solutions. The obtained conditions are expressed in terms of algebraic equations whose feasibility can be checked easily by a simple calculus. Furthermore, we have collated our effort with foregoing one in the available literatures and showed that it is less conserved. Finally, two numerical examples show the feasibility of our theoretical outcomes.

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Acknowledgements

We would like to thank Prof. Dr. Haydar Akca and 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

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

    Adnène Arbi

  3. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China

    Yingxin Guo

  4. 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. Yingxin Guo
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  3. Jinde Cao
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Correspondence to Adnène Arbi.

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Arbi, A., Guo, Y. & Cao, J. Convergence analysis on time scales for HOBAM neural networks in the Stepanov-like weighted pseudo almost automorphic space. Neural Comput & Applic 33, 3567–3581 (2021). https://doi.org/10.1007/s00521-020-05183-0

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  • DOI: https://doi.org/10.1007/s00521-020-05183-0

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