IDEAS home Printed from https://ideas.repec.org/a/hin/complx/3826729.html
   My bibliography  Save this article

Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

Author

Listed:
  • Xiaohui Xu
  • Jiye Zhang
  • Quan Xu
  • Zilong Chen
  • Weifan Zheng

Abstract

This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of -matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.

Suggested Citation

  • Xiaohui Xu & Jiye Zhang & Quan Xu & Zilong Chen & Weifan Zheng, 2017. "Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays," Complexity, Hindawi, vol. 2017, pages 1-12, October.
    • Handle: RePEc:hin:complx:3826729
    DOI: 10.1155/2017/3826729
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2017/3826729.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2017/3826729.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2017/3826729?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. Li, Liangliang & Jian, Jigui, 2015. "Exponential p-convergence analysis for stochastic BAM neural networks with time-varying and infinite distributed delays," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 860-873.
    2. Xiaohui Xu & Jiye Zhang & Jizhong Shi, 2017. "Dynamical behaviour analysis of delayed complex-valued neural networks with impulsive effect," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 686-694, March.
    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. Xiaohui Xu & Huanbin Xue & Yiqiang Peng & Quan Xu & Jibin Yang, 2018. "Robust Exponential Stability of Switched Complex-Valued Neural Networks with Interval Parameter Uncertainties and Impulses," Complexity, Hindawi, vol. 2018, pages 1-12, December.
    2. 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.
    3. Xiaohui Xu & Jibin Yang & Yanhai Xu, 2019. "Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays," Complexity, Hindawi, vol. 2019, pages 1-20, June.

    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. Xiaohui Xu & Jibin Yang & Yanhai Xu, 2019. "Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays," Complexity, Hindawi, vol. 2019, pages 1-20, June.
    2. Zhao, Yongshun & Li, Xiaodi & Cao, Jinde, 2020. "Global exponential stability for impulsive systems with infinite distributed delay based on flexible impulse frequency," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. Jian, Jigui & Wang, Baoxian, 2015. "Global Lagrange stability for neutral-type Cohen–Grossberg BAM neural networks with mixed time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 116(C), pages 1-25.
    4. Wang, Pengfei & Zou, Wenqing & Su, Huan, 2019. "Stability of complex-valued impulsive stochastic functional differential equations on networks with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 338-354.
    5. 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).
    6. Xue, Huanbin & Xu, Xiaohui & Zhang, Jiye & Yang, Xiaopeng, 2019. "Robust stability of impulsive switched neural networks with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 456-475.
    7. Jian, Jigui & Wu, Kai & Wang, Baoxian, 2020. "Global Mittag-Leffler boundedness and synchronization for fractional-order chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    8. Nagamani, G. & Ramasamy, S., 2016. "Stochastic dissipativity and passivity analysis for discrete-time neural networks with probabilistic time-varying delays in the leakage term," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 237-257.
    9. Xiaohui Xu & Huanbin Xue & Yiqiang Peng & Quan Xu & Jibin Yang, 2018. "Robust Exponential Stability of Switched Complex-Valued Neural Networks with Interval Parameter Uncertainties and Impulses," Complexity, Hindawi, vol. 2018, pages 1-12, December.
    10. Yajuan Li & Huanbin Xue, 2024. "Robust Stability Analysis of Switched Neural Networks with Application in Psychological Counseling Evaluation System," Mathematics, MDPI, vol. 12(13), pages 1-21, July.

    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:3826729. 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.