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Finite-Time and Fixed-Time Synchronization of Complex-Valued Recurrent Neural Networks with Discontinuous Activations and Time-Varying Delays

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Abstract

This paper is concerned with finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays. First, by separating the complex-valued recurrent neural networks into real and imaginary parts, we get subsystems with real values covered by the framework of differential inclusions, and novel time-delays feedback controllers are constructed to understand the synchronization problem in finite time and fixed time of error system. Second, by creating Lyapunov functions and applying some differential inequalities, several new criteria are derived to get the synchronization in finite time and fixed time of the studied neural networks. Finally, two numerical examples are presented to justify the effectiveness of our results.

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Authors and Affiliations

  1. Research Units of Mathematics and Applications UR13ES47, Department of Mathematics, Faculty of Sciences of Bizerta, University of Carthage, 7021, Zarzouna, Bizerta, Tunisia

    Chaouki Aouiti & Mayssa Bessifi

  2. School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, Shandong, China

    Xiaodi Li

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  1. Chaouki Aouiti
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  2. Mayssa Bessifi
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  3. Xiaodi Li
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Correspondence to Chaouki Aouiti.

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Aouiti, C., Bessifi, M. & Li, X. Finite-Time and Fixed-Time Synchronization of Complex-Valued Recurrent Neural Networks with Discontinuous Activations and Time-Varying Delays. Circuits Syst Signal Process 39, 5406–5428 (2020). https://doi.org/10.1007/s00034-020-01428-4

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