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Uniformly stable and attractive of fractional-order memristor-based neural networks with multiple delays

Author

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  • Yao, Xueqi
  • Zhong, Shouming
  • Hu, Taotao
  • Cheng, Hong
  • Zhang, Dian

Abstract

Memristive neural networks (MNN) have been wildly studied. Nevertheless, fractional -order memristive neural networks (FMNN) still remain a wide-open dilemma. This paper addresses the problem of FMNN systems with multiple delays and grew several related theories through the study. First, the existence of the system equilibrium point is investigated based on contraction mapping principle, and a new sufficient criterion is obtained. Second, the delay-free uniform stability of the system is discussed by employing differential inclusion theory. Third, a novel asymptotic stability criterion is proposed which is less conservative. Finally, one descriptive numerical example and simulation results emphasize the accuracy and reliability of the proposed results.

Suggested Citation

  • Yao, Xueqi & Zhong, Shouming & Hu, Taotao & Cheng, Hong & Zhang, Dian, 2019. "Uniformly stable and attractive of fractional-order memristor-based neural networks with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 392-403.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:392-403
    DOI: 10.1016/j.amc.2018.11.028
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    References listed on IDEAS

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    1. Zhang, Ruimei & Zeng, Deqiang & Zhong, Shouming & Yu, Yongbin, 2017. "Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 57-74.
    2. Yin, Chun & Zhong, Shou-ming & Huang, Xuegang & Cheng, Yuhua, 2015. "Robust stability analysis of fractional-order uncertain singular nonlinear system with external disturbance," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 351-362.
    3. 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.
    4. Yuping Cao & Chuanzhi Bai, 2014. "Finite-Time Stability of Fractional-Order BAM Neural Networks with Distributed Delay," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, April.
    5. Zeng, Deqiang & Zhang, Ruimei & Liu, Yajuan & Zhong, Shouming, 2017. "Sampled-data synchronization of chaotic Lur’e systems via input-delay-dependent-free-matrix zero equality approach," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 34-46.
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    Cited by:

    1. 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.
    2. Huang, Chengdai & Liu, Heng & Chen, Xiaoping & Zhang, Minsong & Ding, Ling & Cao, Jinde & Alsaedi, Ahmed, 2020. "Dynamic optimal control of enhancing feedback treatment for a delayed fractional order predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).

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