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Dynamical behaviors analysis of memristor-based fractional-order complex-valued neural networks with time delay

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  • Zhang, Yuting
  • Yu, Yongguang
  • Cui, Xueli

Abstract

The robust stability for memristor-based fractional-order Complex-Valued Neural Networks (FCVNNs) with time delay is investigated here. In complex plane, by using the Lyapunov method, and under the sense of Filippov solutions, the existence of unique equilibrium and globally asymptotic stability for such Neural Networks (NNs) have been obtained when the nonlinear complex-valued activation functions could be split into two(real and imaginary) parts. Moreover, locally asymptotic stability for such Neural NNs have been proposed when the nonlinear complex activation functions are bounded. Lastly, three numerical examples are given to confirm the efficiency of theorems.

Suggested Citation

  • Zhang, Yuting & Yu, Yongguang & Cui, Xueli, 2018. "Dynamical behaviors analysis of memristor-based fractional-order complex-valued neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 242-258.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:242-258
    DOI: 10.1016/j.amc.2018.06.042
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    References listed on IDEAS

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    1. Zhang, Lei & Song, Qiankun & Zhao, Zhenjiang, 2017. "Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 296-309.
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    Cited by:

    1. Shuang Wang & Hai Zhang & Weiwei Zhang & Hongmei Zhang, 2021. "Finite-Time Projective Synchronization of Caputo Type Fractional Complex-Valued Delayed Neural Networks," Mathematics, MDPI, vol. 9(12), pages 1-14, June.
    2. Huang, Chengdai & Li, Huan & Cao, Jinde, 2019. "A novel strategy of bifurcation control for a delayed fractional predator–prey model," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 808-838.
    3. Xu, Yao & Li, Wenxue, 2020. "Finite-time synchronization of fractional-order complex-valued coupled systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    4. Pahnehkolaei, Seyed Mehdi Abedi & Alfi, Alireza & Machado, J.A. Tenreiro, 2019. "Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 278-293.

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