IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v39y2009i1p440-453.html
   My bibliography  Save this article

Global exponential stability of a class of retarded impulsive differential equations with applications

Author

Listed:
  • Xia, Yonghui
  • Wong, Patricia J.Y.

Abstract

This paper studies the dynamics of a class of retarded impulsive differential equations (IDE), which generalizes the delayed cellular neural networks (DCNN), delayed bidirectional associative memory (BAM) neural networks and some population growth models. Some sufficient criteria are obtained for the existence and global exponential stability of a unique equilibrium. When the impulsive jumps are absent, our results reduce to its corresponding results for the non-impulsive systems. The approaches are based on Banach’s fixed point theorem, matrix theory and its spectral theory. Due to this method, our results generalize and improve many previous known results such as [3,5,6,9,17,18,23,32,38,43,51,52]. Some examples are also included to illustrate the feasibility and effectiveness of the results obtained.

Suggested Citation

  • Xia, Yonghui & Wong, Patricia J.Y., 2009. "Global exponential stability of a class of retarded impulsive differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 440-453.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:1:p:440-453
    DOI: 10.1016/j.chaos.2007.04.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907003128
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.04.005?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, Chuangxia & Huang, Lihong & Yuan, Zhaohui, 2005. "Global stability analysis of a class of delayed cellular neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(3), pages 133-148.
    2. Liu, Bingwen & Huang, Lihong, 2007. "Existence and exponential stability of almost periodic solutions for cellular neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 95-103.
    3. Xia, Yonghui & Cao, Jinde & Huang, Zhenkun, 2007. "Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1599-1607.
    4. Wang, Zidong & Shu, Huisheng & Liu, Yurong & Ho, Daniel W.C. & Liu, Xiaohui, 2006. "Robust stability analysis of generalized neural networks with discrete and distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 886-896.
    5. Xia, Yonghui & Huang, Zhenkun & Han, Maoan, 2008. "Existence and globally exponential stability of equilibrium for BAM neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 588-597.
    6. Li, Yongkun, 2005. "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 279-285.
    7. Liu, Bingwen & Huang, Lihong, 2007. "Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 211-217.
    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. Berezansky, Leonid & Braverman, Elena, 2015. "Stability conditions for scalar delay differential equations with a non-delay term," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 157-164.
    2. Berezansky, Leonid & Braverman, Elena, 2016. "Boundedness and persistence of delay differential equations with mixed nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 154-169.
    3. Huo, Hai-Feng & Li, Wan-Tong, 2009. "Dynamics of continuous-time bidirectional associative memory neural networks with impulses and their discrete counterparts," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2218-2229.

    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. Huang, Zhenkun & Xia, Yonghui, 2009. "Exponential periodic attractor of impulsive BAM networks with finite distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 373-384.
    2. Wang, Jiafu & Huang, Lihong, 2012. "Almost periodicity for a class of delayed Cohen–Grossberg neural networks with discontinuous activations," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1157-1170.
    3. Zhao, Weirui & Zhang, Huanshui, 2009. "New results of almost periodic solutions for cellular neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 831-838.
    4. Kashkynbayev, Ardak & Cao, Jinde & Suragan, Durvudkhan, 2021. "Global Lagrange stability analysis of retarded SICNNs," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Sun, Yeong-Jeu, 2009. "Global exponential stability criterion for uncertain discrete-time cellular neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2022-2024.
    6. Ninghua Chen, 2013. "Existence of Periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Neutral Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-8, October.
    7. Huang, Zaitang & Yang, Qi-Gui, 2009. "Existence and exponential stability of almost periodic solution for stochastic cellular neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 773-780.
    8. Yu, Jiali & Yi, Zhang & Zhang, Lei, 2009. "Periodicity of a class of nonlinear fuzzy systems with delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1343-1351.
    9. Wang, Xiaohu & Xu, Daoyi, 2009. "Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2713-2721.
    10. 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.
    11. 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.
    12. Li, Kelin & Zeng, Huanglin, 2010. "Stability in impulsive Cohen–Grossberg-type BAM neural networks with time-varying delays: A general analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2329-2349.
    13. 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.
    14. Rakkiyappan, R. & Balasubramaniam, P., 2009. "LMI conditions for stability of stochastic recurrent neural networks with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1688-1696.
    15. Ping, Zhao Wu & Lu, Jun Guo, 2009. "Global exponential stability of impulsive Cohen–Grossberg neural networks with continuously distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 164-174.
    16. Zhao, Weirui, 2009. "On existence and global exponential stability of periodic solution of two-neuron networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1100-1105.
    17. Li, Demin & Wang, Zidong & Zhou, Jie & Fang, Jian’an & Ni, Jinjin, 2008. "A note on chaotic synchronization of time-delay secure communication systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1217-1224.
    18. 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.
    19. Song, Qiankun & Wang, Zidong, 2008. "Neural networks with discrete and distributed time-varying delays: A general stability analysis," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1538-1547.
    20. 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.

    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:eee:chsofr:v:39:y:2009:i:1:p:440-453. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.