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Hybrid Control Scheme for Projective Lag Synchronization of Riemann–Liouville Sense Fractional Order Memristive BAM NeuralNetworks with Mixed Delays

Author

Listed:
  • Grienggrai Rajchakit

    (Department of Mathematics, Maejo University, Chiangmai 50290, Thailand)

  • Anbalagan Pratap

    (Vel Tech High Tech Dr Rangarajan Dr Sakunthala Engineering College, Avadi 600 062, India)

  • Ramachandran Raja

    (Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630 004, India)

  • Jinde Cao

    (School of Mathematics, Southeast University, Nanjing 211189, China)

  • Jehad Alzabut

    (Department of Mathematics and General Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia)

  • Chuangxia Huang

    (Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Department of Applied Mathematics, Changsha University of Science and Technology, Changsha 410114, China)

Abstract

This sequel is concerned with the analysis of projective lag synchronization of Riemann–Liouville sense fractional order memristive BAM neural networks (FOMBNNs) with mixed time delays via hybrid controller. Firstly, a new type of hybrid control scheme, which is the combination of open loop control and adaptive state feedback control is designed to guarantee the global projective lag synchronization of the addressed FOMBNNs model. Secondly, by using a Lyapunov–Krasovskii functional and Barbalet’s lemma, a new brand of sufficient criterion is proposed to ensure the projective lag synchronization of the FOMBNNs model considered. Moreover, as special cases by using a hybrid control scheme, some sufficient conditions are derived to ensure the global projective synchronization, global complete synchronization and global anti-synchronization for the FOMBNNs model considered. Finally, numerical simulations are provided to check the accuracy and validity of our obtained synchronization results.

Suggested Citation

  • Grienggrai Rajchakit & Anbalagan Pratap & Ramachandran Raja & Jinde Cao & Jehad Alzabut & Chuangxia Huang, 2019. "Hybrid Control Scheme for Projective Lag Synchronization of Riemann–Liouville Sense Fractional Order Memristive BAM NeuralNetworks with Mixed Delays," Mathematics, MDPI, vol. 7(8), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:759-:d:258903
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    References listed on IDEAS

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    Cited by:

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    2. Peng, Qiu & Jian, Jigui, 2023. "Synchronization analysis of fractional-order inertial-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 62-77.
    3. Rajchakit, G. & Sriraman, R. & Lim, C.P. & Unyong, B., 2022. "Existence, uniqueness and global stability of Clifford-valued neutral-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 508-527.
    4. Xiao, Shasha & Wang, Zhanshan & Ma, Lei, 2023. "Synchronization Analysis of Fractional Order Delayed BAM Neural Networks via Multi-Delay-Boundary Inequality," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    5. Wang, Chen & Zhang, Hai & Ye, Renyu & Zhang, Weiwei & Zhang, Hongmei, 2023. "Finite time passivity analysis for Caputo fractional BAM reaction–diffusion delayed neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 424-443.
    6. Iswarya, M. & Raja, R. & Cao, J. & Niezabitowski, M. & Alzabut, J. & Maharajan, C., 2022. "New results on exponential input-to-state stability analysis of memristor based complex-valued inertial neural networks with proportional and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 440-461.
    7. Gan, Binbin & Chen, Hao & Xu, Biao & Kang, Wei, 2023. "A norm stability condition of neutral-type Cohen-Grossberg neural networks with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    8. Zhang, Xiulan & Liu, YiYu & Qiu, Hongling & Liu, Heng, 2024. "Dissipativity and synchronization of fractional-order output-coupled neural networks with multiple adaptive coupling weights," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 306-322.

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