IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v40y2009i3p1423-1427.html
   My bibliography  Save this article

Periodic solution for nonautonomous cellular neural networks with impulses

Author

Listed:
  • Sun, Jitao
  • Wang, Qing-Guo
  • Gao, Hanqiao

Abstract

In this paper, we study existence, uniqueness and global stability of periodic solution (i.e., stationary oscillation) for general nonautonomous cellular neural networks with impulses. Some criteria are obtained for stationary oscillation of the nonautonomous cellular neural networks with impulses. It is derived by using a new method which is different from those of the previous literatures. Previous results are extended and improved. An illustrative example is given to demonstrate the effectiveness and less conservativeness of the obtained results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1423-1427
    DOI: 10.1016/j.chaos.2007.09.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907007631
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.09.027?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. Song, Qiankun, 2008. "Novel criteria for global exponential periodicity and stability of recurrent neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 720-728.
    2. Li, Chuandong & Liao, Xiaofeng & Zhang, Rong & Prasad, Ashutosh, 2005. "Global robust exponential stability analysis for interval neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 751-757.
    3. Zheng, Baodong & Zhang, Yazhuo & Zhang, Chunrui, 2008. "Global existence of periodic solutions on a simplified BAM neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1397-1408.
    4. Gui, Zhanji & Ge, Weigao, 2007. "Periodic solutions of nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1760-1771.
    5. Lou, Xuyang & Cui, Baotong & Wu, Wei, 2008. "On global exponential stability and existence of periodic solutions for BAM neural networks with distributed delays and reaction–diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 1044-1054.
    6. Yuan, Kun & Cao, Jinde, 2006. "Periodic oscillatory solution in delayed competitive–cooperative neural networks: A decomposition approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 223-231.
    7. 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.
    8. Li, Yongkun & Xing, Wenya & Lu, Linghong, 2006. "Existence and global exponential stability of periodic solution of a class of neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 437-445.
    9. Mohamad, Sannay, 2007. "Exponential stability in Hopfield-type neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 456-467.
    10. Xiong, Wanmin & Zhou, Qiyuan & Xiao, Bing & Yu, Yuehua, 2007. "Global exponential stability of cellular neural networks with mixed delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 896-902.
    11. Wang, Hui & Liao, Xiaofeng & Li, Chuandong, 2007. "Existence and exponential stability of periodic solution of BAM neural networks with impulse and time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1028-1039.
    12. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2005. "Delay-dependent exponential stability of cellular neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1363-1369.
    13. Li, Yongkun & Xing, Zhiwei, 2007. "Existence and global exponential stability of periodic solution of CNNs with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1686-1693.
    14. Li, Ping & Cao, Jinde & Wang, Zidong, 2007. "Robust impulsive synchronization of coupled delayed neural networks with uncertainties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 261-272.
    15. Chen, Zhang & Ruan, Jiong, 2007. "Global dynamic analysis of general Cohen–Grossberg neural networks with impulse," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1830-1837.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. Li, Yongkun & Xing, Zhiwei, 2007. "Existence and global exponential stability of periodic solution of CNNs with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1686-1693.
    4. Yang, Yu & Ye, Jin, 2009. "Stability and bifurcation in a simplified five-neuron BAM neural network with delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2357-2363.
    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. Li, Chun-Hsien & Yang, Suh-Yuh, 2009. "Existence and attractivity of periodic solutions to non-autonomous Cohen–Grossberg neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1235-1244.
    7. Zhang, Yinping, 2009. "Stationary oscillation for nonautonomous bidirectional associative memory neural networks with impulse," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1760-1763.
    8. Chen, Zhang, 2009. "Dynamic analysis of reaction–diffusion Cohen–Grossberg neural networks with varying delay and Robin boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1724-1730.
    9. Huang, Zai-Tang & Luo, Xiao-Shu & Yang, Qi-Gui, 2007. "Global asymptotic stability analysis of bidirectional associative memory neural networks with distributed delays and impulse," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 878-885.
    10. Luo, Wenpin & Zhong, Shouming & Yang, Jun, 2009. "Global exponential stability of impulsive Cohen–Grossberg neural networks with delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1084-1091.
    11. Xu, Liguang & Xu, Daoyi, 2009. "Exponential p-stability of impulsive stochastic neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 263-272.
    12. He, Yong & Wang, Qing-Guo & Zheng, Wei-Xing, 2005. "Global robust stability for delayed neural networks with polytopic type uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1349-1354.
    13. Park, Ju H. & Lee, S.M. & Kwon, O.M., 2009. "On exponential stability of bidirectional associative memory neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1083-1091.
    14. Singh, Vimal, 2007. "Global asymptotic stability of neural networks with delay: Comparative evaluation of two criteria," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1187-1190.
    15. Gau, R.S. & Lien, C.H. & Hsieh, J.G., 2007. "Global exponential stability for uncertain cellular neural networks with multiple time-varying delays via LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1258-1267.
    16. Li, Dong & Yang, Dan & Wang, Hui & Zhang, Xiaohong & Wang, Shilong, 2009. "Asymptotical stability of multi-delayed cellular neural networks with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 218-224.
    17. Mak, K.L. & Peng, J.G. & Xu, Z.B. & Yiu, K.F.C., 2007. "A new stability criterion for discrete-time neural networks: Nonlinear spectral radius," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 424-436.
    18. Gui, Zhanji & Ge, Weigao, 2007. "Periodic solutions of nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1760-1771.
    19. Lien, Chang-Hua & Chung, Long-Yeu, 2007. "Global asymptotic stability for cellular neural networks with discrete and distributed time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1213-1219.
    20. 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.

    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:40:y:2009:i:3:p:1423-1427. 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.