IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v373y2020ics0096300319310124.html
   My bibliography  Save this article

Global Mittag-Leffler synchronization of fractional-order delayed quaternion-valued neural networks: Direct quaternion approach

Author

Listed:
  • Li, Hong-Li
  • Zhang, Long
  • Hu, Cheng
  • Jiang, Haijun
  • Cao, Jinde

Abstract

This paper investigates the global Mittag-Leffler synchronization (GMLS) issue for fractional-order delayed quaternion-valued neural networks, which include leakage delays and transmission delays. First, a new lemma is established to estimate the Caputo fractional derivative for quaternion self-conjugate quadratic Lyapunov function, and a novel quaternion-valued linear feedback controller is designed. Then by utilizing quaternion matrix theory and our proposed lemma, some succinct GMLS criteria are derived respectively in quaternion-valued linear matrix inequality (LMI) form and complex-valued LMI form, which simplify and extend some previous work on the synchronization control for quaternion-value neural networks. Finally, a numerical example is given to validate our theoretical results.

Suggested Citation

  • Li, Hong-Li & Zhang, Long & Hu, Cheng & Jiang, Haijun & Cao, Jinde, 2020. "Global Mittag-Leffler synchronization of fractional-order delayed quaternion-valued neural networks: Direct quaternion approach," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    • Handle: RePEc:eee:apmaco:v:373:y:2020:i:c:s0096300319310124
    DOI: 10.1016/j.amc.2019.125020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319310124
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.125020?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
    2. Li, Hong-Li & Jiang, Yao-Lin & Wang, Zuolei & Zhang, Long & Teng, Zhidong, 2015. "Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 269-277.
    3. Qi, Xingnan & Bao, Haibo & Cao, Jinde, 2019. "Exponential input-to-state stability of quaternion-valued neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 382-393.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhao, Mingfang & Li, Hong-Li & Zhang, Long & Hu, Cheng & Jiang, Haijun, 2023. "Quasi-synchronization of discrete-time fractional-order quaternion-valued memristive neural networks with time delays and uncertain parameters," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    2. Shu, Jinlong & Wu, Baowei & Xiong, Lianglin, 2022. "Stochastic stability criteria and event-triggered control of delayed Markovian jump quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    3. Zhang, Hai & Cheng, Yuhong & Zhang, Hongmei & Zhang, Weiwei & Cao, Jinde, 2022. "Hybrid control design for Mittag-Leffler projective synchronization on FOQVNNs with multiple mixed delays and impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 341-357.
    4. Zheng, Bibo & Wang, Zhanshan, 2022. "Mittag-Leffler synchronization of fractional-order coupled neural networks with mixed delays," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    5. Yang, Shuai & Hu, Cheng & Yu, Juan & Jiang, Haijun, 2021. "Projective synchronization in finite-time for fully quaternion-valued memristive networks with fractional-order," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    6. Li, Hui & Kao, YongGui & Stamova, Ivanka & Shao, Chuntao, 2021. "Global asymptotic stability and S-asymptotic ω-periodicity of impulsive non-autonomous fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 410(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Hong-Li & Kao, Yonggui & Hu, Cheng & Jiang, Haijun & Jiang, Yao-Lin, 2021. "Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. 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.
    3. Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    4. Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability," Mathematics, MDPI, vol. 8(5), pages 1-26, May.
    5. Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks," Mathematics, MDPI, vol. 8(5), pages 1-27, May.
    6. 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.
    7. Grienggrai Rajchakit & Pharunyou Chanthorn & Pramet Kaewmesri & Ramalingam Sriraman & Chee Peng Lim, 2020. "Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks," Mathematics, MDPI, vol. 8(3), pages 1-29, March.
    8. Tu, Zhengwen & Ding, Nan & Li, Liangliang & Feng, Yuming & Zou, Limin & Zhang, Wei, 2017. "Adaptive synchronization of memristive neural networks with time-varying delays and reaction–diffusion term," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 118-128.
    9. Jiang, Xiaowei & Chen, Xiangyong & Chi, Ming & Chen, Jie, 2020. "On Hopf bifurcation and control for a delay systems," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    10. Wang, Xinhe & Lu, Junwei & Wang, Zhen & Li, Yuxia, 2020. "Dynamics of discrete epidemic models on heterogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    11. Zhang, Zhengqiu & Yang, Zhen, 2023. "Asymptotic stability for quaternion-valued fuzzy BAM neural networks via integral inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    12. Pan, Jie & Pan, Zhaoya, 2021. "Novel robust stability criteria for uncertain parameter quaternionic neural networks with mixed delays: Whole quaternionic method," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    13. Jin-E Zhang, 2017. "Centralized and Decentralized Data-Sampling Principles for Outer-Synchronization of Fractional-Order Neural Networks," Complexity, Hindawi, vol. 2017, pages 1-11, March.
    14. Wang, Huanan & Huang, Chengdai & Liu, Heng & Cao, Jinde, 2023. "Detecting bifurcations in a fractional-order neural network with nonidentical delays via Cramer’s rule," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    15. 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.
    16. Chen, Wei & Yu, Yongguang & Hai, Xudong & Ren, Guojian, 2022. "Adaptive quasi-synchronization control of heterogeneous fractional-order coupled neural networks with reaction-diffusion," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    17. Chen, Shenglong & Yang, Jikai & Li, Zhiming & Li, Hong-Li & Hu, Cheng, 2023. "New results for dynamical analysis of fractional-order gene regulatory networks with time delay and uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    18. Zhang, Weiwei & Sha, Chunlin & Cao, Jinde & Wang, Guanglan & Wang, Yuan, 2021. "Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    19. Baluni, Sapna & Sehgal, Ishani & Yadav, Vijay K. & Das, Subir, 2024. "Exponential synchronization of a class of quaternion-valued neural network with time-varying delays: A Matrix Measure Approach," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    20. Ali Yousef & Fatma Bozkurt Yousef, 2019. "Bifurcation and Stability Analysis of a System of Fractional-Order Differential Equations for a Plant–Herbivore Model with Allee Effect," Mathematics, MDPI, vol. 7(5), pages 1-18, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:373:y:2020:i:c:s0096300319310124. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.