IDEAS home Printed from https://ideas.repec.org/a/hin/complx/6751806.html
   My bibliography  Save this article

Existence and Global Exponential Stability of Almost Automorphic Solution for Clifford-Valued High-Order Hopfield Neural Networks with Leakage Delays

Author

Listed:
  • Bing Li
  • Yongkun Li

Abstract

In this paper, we study the existence and global exponential stability of almost automorphic solutions for Clifford-valued high-order Hopfield neural networks by direct method. That is to say, we do not decompose the systems under consideration into real-valued systems, but we directly study Clifford-valued systems. Our methods and results are new. Finally, an example is given to illustrate our main results.

Suggested Citation

  • Bing Li & Yongkun Li, 2019. "Existence and Global Exponential Stability of Almost Automorphic Solution for Clifford-Valued High-Order Hopfield Neural Networks with Leakage Delays," Complexity, Hindawi, vol. 2019, pages 1-13, July.
    • Handle: RePEc:hin:complx:6751806
    DOI: 10.1155/2019/6751806
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/6751806.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/6751806.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/6751806?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
    ---><---

    References listed on IDEAS

    as
    1. Yongkun Li & Xiaofang Meng, 2017. "Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Quaternion-Valued Neural Networks with Delays in the Leakage Term on Time Scales," Complexity, Hindawi, vol. 2017, pages 1-15, December.
    2. Yongkun Li & Jianglian Xiang, 2019. "Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNNs with Discrete Delays," Complexity, Hindawi, vol. 2019, pages 1-13, May.
    3. Liu, Jiang, 2005. "Global exponential stability of Cohen–Grossberg neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 935-945.
    4. Xu, Changjin & Li, Peiluan, 2017. "Global exponential convergence of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 139-144.
    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. 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.
    2. 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).
    3. Suriguga, & Kao, Yonggui & Shao, Chuntao & Chen, Xiangyong, 2021. "Stability of high-order delayed Markovian jumping reaction-diffusion HNNs with uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    4. Li, Yongkun & Wang, Xiaohui, 2021. "Almost periodic solutions in distribution of Clifford-valued stochastic recurrent neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).

    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. 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.
    2. Bing Li & Yongkun Li & Xiaofang Meng, 2019. "The Existence and Global Exponential Stability of Almost Periodic Solutions for Neutral-Type CNNs on Time Scales," Mathematics, MDPI, vol. 7(4), pages 1-25, March.
    3. Lu Pang & Cheng Hu & Juan Yu & Haijun Jiang, 2022. "Fixed-Time Synchronization for Fuzzy-Based Impulsive Complex Networks," Mathematics, MDPI, vol. 10(9), pages 1-16, May.
    4. Mohamad, Sannay, 2008. "Computer simulations of exponentially convergent networks with large impulses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 331-344.
    5. Chen, Ling & Zhao, Hongyong, 2008. "Global stability of almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 351-357.
    6. Sun, Yeong-Jeu, 2007. "Duality between observation and output feedback for linear systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 879-884.
    7. Xia, Yonghui & Huang, Zhenkun & Han, Maoan, 2008. "Exponential p-stability of delayed Cohen–Grossberg-type BAM neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 806-818.
    8. Li, Chun-Hsien & Yang, Suh-Yuh, 2007. "A further analysis on harmless delays in Cohen–Grossberg neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 646-653.
    9. 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.
    10. Yongkun Li & Xiaofang Meng, 2017. "Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Quaternion-Valued Neural Networks with Delays in the Leakage Term on Time Scales," Complexity, Hindawi, vol. 2017, pages 1-15, December.
    11. 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).
    12. 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.
    13. Yongkun Li & Xiaofang Meng & Yuan Ye, 2018. "Almost Periodic Synchronization for Quaternion-Valued Neural Networks with Time-Varying Delays," Complexity, Hindawi, vol. 2018, pages 1-13, April.
    14. Huang, Chuangxia & Liu, Bingwen & Qian, Chaofan & Cao, Jinde, 2021. "Stability on positive pseudo almost periodic solutions of HPDCNNs incorporating D operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1150-1163.
    15. Wen, Zhen & Sun, Jitao, 2009. "Stability analysis of delayed Cohen–Grossberg BAM neural networks with impulses via nonsmooth analysis," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1829-1837.
    16. Sun, Jitao & Wang, Qing-Guo & Gao, Hanqiao, 2009. "Periodic solution for nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1423-1427.
    17. Huang, Tingwen & Li, Chuandong & Chen, Goong, 2007. "Stability of Cohen–Grossberg neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 992-996.
    18. Sun, Yeong-Jeu, 2009. "Stability criteria for a class of differential inclusion systems with discrete and distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2386-2391.
    19. Liu, Hailin & Chen, Guohua, 2007. "Delay-dependent stability for neural networks with time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 171-177.
    20. Liu, Bingwen, 2007. "Almost periodic solutions for Hopfield neural networks with continuously distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(5), pages 327-335.

    More about this item

    Statistics

    Access and download statistics

    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:hin:complx:6751806. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.