Articles

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

  • Anbalagan PRATAP ,
  • Ramachandran RAJA ,
  • Jinde CAO ,
  • Chuangxia HUANG ,
  • Chuangxia HUANG ,
  • Ovidiu BAGDASAR
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  • 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 date: 2020-06-11

  Revised date: 2021-06-09

  Online published: 2022-08-23

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.

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.

Cite this article

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 . DOI: 10.1007/s10473-022-0402-7

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