$\mathcal{O}(t^{-\beta})$-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

doi:10.1007/s10473-022-0402-7

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (4): 1273-1292.doi: 10.1007/s10473-022-0402-7

$\mathcal{O}(t^{-\beta})$-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

Anbalagan PRATAP¹, Ramachandran RAJA², 曹进德^3,4, 黃创霞⁵, Chuangxia HUANG⁶, Ovidiu BAGDASAR⁷

1. Department of Mathematics, Alagappa University, Tamil Nadu, Karaikudi, 630004, India;
2. Ramanujan Centre for Higher Mathematics, Alagappa University, Tamil Nadu, Karaikudi, 630004, India;
3. School of Mathematics, Southeast University, Nanjing, 211189, China;
4. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea;
5. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114, China;
6. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 12435, Saudi Arabia;
7. Department of Electronics, Computing and Mathematics, University of Derby, Derby, UK

收稿日期:2020-06-11 修回日期:2021-06-09 出版日期:2022-08-25 发布日期:2022-08-23
通讯作者: Jinde CAO,E-mail:jdcao@seu.edu.cn;Chuangxia HUANG,E-mail:cxiahuang@csust.edu.cn E-mail:jdcao@seu.edu.cn;cxiahuang@csust.edu.cn
基金资助:
This article has been written with the joint financial support of Thailand Research Fund RSA 6280004, RUSA-Phase 2.0 Grant No.F 24-51/2014-U, Policy (TN Multi-Gen), Dept. of Edn. Govt. of India, UGC-SAP (DRS-I) Grant No.F.510/8/DRS-I/2016(SAP-I), DST (FIST-level I) 657876570 Grant No.SR/FIST/MS-I/2018/17 and Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17.

$\mathcal{O}(t^{-\beta})$-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

Anbalagan PRATAP¹, Ramachandran RAJA², Jinde CAO^3,4, Chuangxia HUANG⁵, Chuangxia HUANG⁶, Ovidiu BAGDASAR⁷

1. Department of Mathematics, Alagappa University, Tamil Nadu, Karaikudi, 630004, India;
2. Ramanujan Centre for Higher Mathematics, Alagappa University, Tamil Nadu, Karaikudi, 630004, India;
3. School of Mathematics, Southeast University, Nanjing, 211189, China;
4. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea;
5. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114, China;
6. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 12435, Saudi Arabia;
7. Department of Electronics, Computing and Mathematics, University of Derby, Derby, UK

Received:2020-06-11 Revised:2021-06-09 Online:2022-08-25 Published:2022-08-23
Contact: Jinde CAO,E-mail:jdcao@seu.edu.cn;Chuangxia HUANG,E-mail:cxiahuang@csust.edu.cn E-mail:jdcao@seu.edu.cn;cxiahuang@csust.edu.cn
Supported by:
This article has been written with the joint financial support of Thailand Research Fund RSA 6280004, RUSA-Phase 2.0 Grant No.F 24-51/2014-U, Policy (TN Multi-Gen), Dept. of Edn. Govt. of India, UGC-SAP (DRS-I) Grant No.F.510/8/DRS-I/2016(SAP-I), DST (FIST-level I) 657876570 Grant No.SR/FIST/MS-I/2018/17 and Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17.

摘要/Abstract

摘要： This article explores the $\mathcal{O}(t^{-\beta})$ synchronization and asymptotic synchronization for fractional order BAM neural networks (FBAMNNs) with discrete delays, distributed delays and non-identical perturbations. By designing a state feedback control law and a new kind of fractional order Lyapunov functional, a new set of algebraic sufficient conditions are derived to guarantee the $\mathcal{O}(t^{-\beta})$ Synchronization and asymptotic synchronization of the considered FBAMNNs model; this can easily be evaluated without using a MATLAB LMI control toolbox. Finally, two numerical examples, along with the simulation results, illustrate the correctness and viability of the exhibited synchronization results.

关键词: $\mathbf{\mathcal{O}(t^{-\beta})}$-synchronization, asymptotic synchronization, BAM neural networks, fractional order, state feedback control law

Abstract: This article explores the $\mathcal{O}(t^{-\beta})$ synchronization and asymptotic synchronization for fractional order BAM neural networks (FBAMNNs) with discrete delays, distributed delays and non-identical perturbations. By designing a state feedback control law and a new kind of fractional order Lyapunov functional, a new set of algebraic sufficient conditions are derived to guarantee the $\mathcal{O}(t^{-\beta})$ Synchronization and asymptotic synchronization of the considered FBAMNNs model; this can easily be evaluated without using a MATLAB LMI control toolbox. Finally, two numerical examples, along with the simulation results, illustrate the correctness and viability of the exhibited synchronization results.

Key words: $\mathbf{\mathcal{O}(t^{-\beta})}$-synchronization, asymptotic synchronization, BAM neural networks, fractional order, state feedback control law

中图分类号:

34K24

Anbalagan PRATAP, Ramachandran RAJA, 曹进德, 黃创霞, Chuangxia HUANG, Ovidiu BAGDASAR. $\mathcal{O}(t^{-\beta})$-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS[J]. 数学物理学报(英文版), 2022, 42(4): 1273-1292.

Anbalagan PRATAP, Ramachandran RAJA, Jinde CAO, Chuangxia HUANG, Chuangxia HUANG, Ovidiu BAGDASAR. $\mathcal{O}(t^{-\beta})$-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS[J]. Acta mathematica scientia,Series B, 2022, 42(4): 1273-1292.

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$\mathcal{O}(t^{-\beta})$-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

$\mathcal{O}(t^{-\beta})$-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

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