Convergence analysis on time scales for HOBAM neural networks in the Stepanov-like weighted pseudo almost automorphic sp
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Convergence analysis on time scales for HOBAM neural networks in the Stepanov-like weighted pseudo almost automorphic space Adne`ne Arbi1,2
•
Yingxin Guo3 • Jinde Cao4
Received: 26 September 2019 / Accepted: 11 July 2020 Ó Springer-Verlag London Ltd., part of Springer Nature 2020
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 Ddynamic 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. Keywords Time scales High-order BAM neural networks Stepanov-like weighted pseudo almost automorphic solution Leakage delays
1 Introduction
& Adne`ne Arbi [email protected] Yingxin Guo [email protected] Jinde Cao [email protected] 1
Laboratory of Engineering Mathematics (LR01ES13), Tunisia Polytechnic School, University of Carthage, Tunis, Tunisia
2
Department of Advanced Sciences and Technologies at National School of Advanced Sciences and Technologies of Borj Cedria, University of Carthage, Tunis, Tunisia
3
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China
4
Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and School of Mathematics, Southeast University, Nanjing, China
The qualitative analysis on time scales of the weighted pseudo almost automorphic type of functions for the nabla and delta derivatives is a natural generalization of almost automorphic on time scales functions introduced in [1]. Moreover, there is no definition of the notion of Stepanovlike almost automorphy and Stepanov-like weighted pseudo almost automorphic (Stepanov-like WPAA) on time scales in the previous works. Many researchers have oriented their works toward the qualitative analysis of different model of neural networks (see [2–6]). Furthermore, BAM neural networks as a special case of neural network (see [7–12]) were firstly introduced by Kosko [13]. Besides, the time delays are important in the modeling of dyn
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