IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v359y2019icp278-293.html
   My bibliography  Save this article

Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition

Author

Listed:
  • Pahnehkolaei, Seyed Mehdi Abedi
  • Alfi, Alireza
  • Machado, J.A. Tenreiro

Abstract

This paper studies the stability of fractional order (FO) continuous-time quaternion-valued Leaky Integrator Echo State Neural Networks (NN). The delay independent robust stability of NN with QUAD vector field activation functions under time varying delays is derived. The analysis follows the FO Lyapunov theorem while decomposing the NN into four real-valued systems. The existence and uniqueness of the equilibrium point are also verified by means of a contraction map on the decomposed NN. The new approach is tested in the stability analysis of the FO quaternion-valued Echo State NN whitout time delays, complex-valued Echo State and quaternion-/complex-valued Hopfield NN with/without time delays. Two numerical examples demonstrate the feasibility of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:278-293
    DOI: 10.1016/j.amc.2019.04.083
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319303856
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.04.083?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. Tan, Manchun & Liu, Yunfeng & Xu, Desheng, 2019. "Multistability analysis of delayed quaternion-valued neural networks with nonmonotonic piecewise nonlinear activation functions," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 229-255.
    3. Zhang, Weiwei & Cao, Jinde & Wu, Ranchao & Chen, Dingyuan & Alsaadi, Fuad E., 2018. "Novel results on projective synchronization of fractional-order neural networks with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 76-83.
    4. 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.
    5. Chang, Wenting & Zhu, Song & Li, Jinyu & Sun, Kaili, 2018. "Global Mittag–Leffler stabilization of fractional-order complex-valued memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 346-362.
    6. 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.
    7. 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.
    8. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    9. Li, Ruoxia & Cao, Jinde & Alsaedi, Ahmad & Alsaadi, Fuad, 2017. "Exponential and fixed-time synchronization of Cohen–Grossberg neural networks with time-varying delays and reaction-diffusion terms," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 37-51.
    10. 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.
    11. 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.
    12. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Alsaadi, Fuad E., 2017. "Controlling bifurcation in a delayed fractional predator–prey system with incommensurate orders," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 293-310.
    13. 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.
    14. Zhang, Jianmei & Wu, Jianwei & Bao, Haibo & Cao, Jinde, 2018. "Synchronization analysis of fractional-order three-neuron BAM neural networks with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 441-450.
    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. Aghayan, Zahra Sadat & Alfi, Alireza & Mousavi, Yashar & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Guaranteed cost robust output feedback control design for fractional-order uncertain neutral delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Liu, Chong & Zhang, Huaguang & Luo, Yanhong & Zhang, Kun, 2021. "Echo state network-based online optimal control for discrete-time nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    3. 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).
    4. Wang, Huamin & Wei, Guoliang & Wen, Shiping & Huang, Tingwen, 2021. "Impulsive disturbance on stability analysis of delayed quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 390(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. 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).
    2. 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).
    3. 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.
    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.
    5. 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).
    6. 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.
    7. Li, Qiaoping & Liu, Sanyang & Chen, Yonggang, 2018. "Combination event-triggered adaptive networked synchronization communication for nonlinear uncertain fractional-order chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 521-535.
    8. 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).
    9. 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).
    10. 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.
    11. 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.
    12. Li, Xing-Yu & Wu, Kai-Ning & Liu, Xiao-Zhen, 2023. "Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems via intermittent boundary control," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    13. 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).
    14. Zhen Yang & Zhengqiu Zhang, 2022. "Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
    15. 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.
    16. Rajchakit, G. & Sriraman, R. & Vignesh, P. & Lim, C.P., 2021. "Impulsive effects on Clifford-valued neural networks with time-varying delays: An asymptotic stability analysis," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    17. Grienggrai Rajchakit & Ramalingam Sriraman & Chee Peng Lim & Panu Sam-ang & Porpattama Hammachukiattikul, 2021. "Synchronization in Finite-Time Analysis of Clifford-Valued Neural Networks with Finite-Time Distributed Delays," Mathematics, MDPI, vol. 9(11), pages 1-18, May.
    18. Lu, Xiaoling & Sun, Weihua, 2024. "Control and synchronization of Julia sets of discrete fractional Ising models," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    19. Li, Donghua & Zhang, Zhengqiu & Zhang, Xiaoluan, 2020. "Periodic solutions of discrete-time Quaternion-valued BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    20. Luo, Yiping & Yao, Yuejie & Cheng, Zifeng & Xiao, Xing & Liu, Hanyu, 2021. "Event-triggered control for coupled reaction–diffusion complex network systems with finite-time synchronization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).

    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:359:y:2019:i:c:p:278-293. 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.