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Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays

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  • Zhang, Lei
  • Song, Qiankun
  • Zhao, Zhenjiang

Abstract

In this paper, the problem of uniform stability for fractional-order complex-valued neural networks with both leakage and discrete delays is considered. Base on the contracting mapping principle, a sufficient condition is proposed for the existence and uniqueness of the equilibrium point of the addressed neural networks. By employing analysis technique, some delay-dependent criteria are established for checking the global uniform stability of the fractional-order complex-valued neural networks. Two numerical examples are presented to demonstrate the validity and feasibility of the proposed results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:298:y:2017:i:c:p:296-309
    DOI: 10.1016/j.amc.2016.11.027
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    References listed on IDEAS

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    1. Liu, Yuji, 2016. "On piecewise continuous solutions of higher order impulsive fractional differential equations and applications," Applied Mathematics and Computation, Elsevier, vol. 287, pages 38-49.
    2. Zeng, Xu & Li, Chuandong & Huang, Tingwen & He, Xing, 2015. "Stability analysis of complex-valued impulsive systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 75-82.
    3. Ji, Meng-Di & He, Yong & Wu, Min & Zhang, Chuan-Ke, 2015. "Further results on exponential stability of neural networks with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 175-182.
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    2. Zhixin Zhang & Yufeng Zhang & Jia-Bao Liu & Jiang Wei, 2019. "Global Asymptotical Stability Analysis for Fractional Neural Networks with Time-Varying Delays," Mathematics, MDPI, vol. 7(2), pages 1-8, February.
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    6. Syed Ali, M. & Narayanan, Govindasamy & Shekher, Vineet & Alsulami, Hamed & Saeed, Tareq, 2020. "Dynamic stability analysis of stochastic fractional-order memristor fuzzy BAM neural networks with delay and leakage terms," Applied Mathematics and Computation, Elsevier, vol. 369(C).
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    8. Panda, Sumati Kumari & Nagy, A.M. & Vijayakumar, Velusamy & Hazarika, Bipan, 2023. "Stability analysis for complex-valued neural networks with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    9. Duan, Lian & Shi, Min & Huang, Chuangxia & Fang, Xianwen, 2021. "Synchronization in finite-/fixed-time of delayed diffusive complex-valued neural networks with discontinuous activations," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    10. Jinman He & Fangqi Chen & Qinsheng Bi, 2019. "Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network," Complexity, Hindawi, vol. 2019, pages 1-15, April.
    11. Zhang, Weiwei & Zhang, Hai & Cao, Jinde & Zhang, Hongmei & Chen, Dingyuan, 2020. "Synchronization of delayed fractional-order complex-valued neural networks with leakage delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    12. Yang, Zhanying & Zhang, Jie & Zhang, Zhihui & Mei, Jun, 2023. "An improved criterion on finite-time stability for fractional-order fuzzy cellular neural networks involving leakage and discrete delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 910-925.
    13. Zhang, Hai & Ye, Miaolin & Ye, Renyu & Cao, Jinde, 2018. "Synchronization stability of Riemann–Liouville fractional delay-coupled complex neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 155-165.
    14. Xu, Quan & Xu, Xiaohui & Zhuang, Shengxian & Xiao, Jixue & Song, Chunhua & Che, Chang, 2018. "New complex projective synchronization strategies for drive-response networks with fractional complex-variable dynamics," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 552-566.
    15. 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.
    16. Mo, Lipo & Yuan, Xiaolin & Yu, Yongguang, 2018. "Target-encirclement control of fractional-order multi-agent systems with a leader," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 479-491.
    17. Jin-E Zhang, 2017. "Multisynchronization for Coupled Multistable Fractional-Order Neural Networks via Impulsive Control," Complexity, Hindawi, vol. 2017, pages 1-10, August.
    18. Hu, Binxin & Song, Qiankun & Zhao, Zhenjiang, 2020. "Robust state estimation for fractional-order complex-valued delayed neural networks with interval parameter uncertainties: LMI approach," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    19. 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.
    20. Zhang, Yanlin & Deng, Shengfu, 2019. "Finite-time projective synchronization of fractional-order complex-valued memristor-based neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 176-190.
    21. Shi, Yanchao & Cao, Jinde & Chen, Guanrong, 2017. "Exponential stability of complex-valued memristor-based neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 222-234.
    22. Tu, Zhengwen & Zhao, Yongxiang & Ding, Nan & Feng, Yuming & Zhang, Wei, 2019. "Stability analysis of quaternion-valued neural networks with both discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 342-353.
    23. Yu Yao & Guodong Zhang & Yan Li, 2023. "Fixed/Preassigned-Time Stabilization for Complex-Valued Inertial Neural Networks with Distributed Delays: A Non-Separation Approach," Mathematics, MDPI, vol. 11(10), pages 1-17, May.

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