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\({\cal O}({t^{ - \beta }})\)-Synchronization and Asymptotic Synchronization of Delayed Fractional Order Neural Networks

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Abstract

This article explores the \({\cal O}({t^{ - \beta }})\) 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 \({\cal O}({t^{ - \beta }})\) 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.

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Authors and Affiliations

  1. Department of Mathematics, Alagappa University, Tamil Nadu, Karaikudi, 630004, India

    Anbalagan Pratap

  2. Ramanujan Centre for Higher Mathematics, Alagappa University, Tamil Nadu, Karaikudi, 630004, India

    Ramachandran Raja

  3. School of Mathematics, Southeast University, Nanjing, 211189, China

    Jinde Cao

  4. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea

    Jinde Cao

  5. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114, China

    Chuangxia Huang

  6. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 12435, Saudi Arabia

    Jehad Alzabut

  7. Department of Electronics, Computing and Mathematics, University of Derby, Derby, UK

    Ovidiu Bagdasar

Authors
  1. Anbalagan Pratap
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  2. Ramachandran Raja
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  3. Jinde Cao
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  4. Chuangxia Huang
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  5. Jehad Alzabut
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  6. Ovidiu Bagdasar
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Corresponding author

Correspondence to Jinde Cao.

Additional information

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.

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Pratap, A., Raja, R., Cao, J. et al. \({\cal O}({t^{ - \beta }})\)-Synchronization and Asymptotic Synchronization of Delayed Fractional Order Neural Networks. Acta Math Sci 42, 1273–1292 (2022). https://doi.org/10.1007/s10473-022-0402-7

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  • DOI: https://doi.org/10.1007/s10473-022-0402-7

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