Finite-Time and Fixed-Time Synchronization of Complex-Valued Recurrent Neural Networks with Discontinuous Activations an
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Finite-Time and Fixed-Time Synchronization of Complex-Valued Recurrent Neural Networks with Discontinuous Activations and Time-Varying Delays Chaouki Aouiti1 · Mayssa Bessifi1 · Xiaodi Li2 Received: 22 April 2019 / Revised: 12 April 2020 / Accepted: 15 April 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper is concerned with finite-time and fixed-time synchronization of complexvalued 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. Keywords Finite-time synchronization · Fixed-time synchronization · Recurrent neural networks · Complex-valued · Discontinuous activations · Differential inclusions
1 Introduction In the last few years, recurrent neural networks (RNNs) have attracted increasing attention from many areas of science and technology because of their extensive applications
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Chaouki Aouiti [email protected] Mayssa Bessifi [email protected] Xiaodi Li [email protected]
1
Research Units of Mathematics and Applications UR13ES47, Department of Mathematics, Faculty of Sciences of Bizerta, University of Carthage, 7021 Zarzouna, Bizerta, Tunisia
2
School of Mathematical Sciences, Shandong Normal University, Jinan 250014, Shandong, China
Circuits, Systems, and Signal Processing
in signal processing, pattern recognition, optimization problems and associative memory [1,4,5,7,9,21,37,47]. It is well known that many of these applications are mainly based on the dynamic behavior of the neural networks (NNs). Therefore, it is extremely indispensable and essential to analyze the dynamics of NNs. On the other hand, discontinuous NNs, in particular, with discontinuous activations, have a significant advantage over traditional NNs models, as they have the capacity to perform the nonlinear mapping. In ideal circumstances, it can approximate many linear and nonlinear relationship. At the same time, it has the self-learning autogenous shrinkage characteristics and has the strong robustness and fault tolerance. Considering this fact, much efforts have been devoted to studying the dynamical properties of neural networks with discontinuous activation, see [17,19,20,44] and the references therein. In addition, because of the theoretical importance and potential applications of NNs with discontinuous activations, time delays, especially time-varying delays, are inevitable because of the limitedness on the speed of sig
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