IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i3p1245-1252.html
   My bibliography  Save this article

A neural network method for solving a system of linear variational inequalities

Author

Listed:
  • Lan, Heng-you
  • Cui, Yi-Shun

Abstract

In this paper, we transmute the solution for a new system of linear variational inequalities to an equilibrium point of neural networks, and by using analytic technique, some sufficient conditions are presented. Further, the estimation of the exponential convergence rates of the neural networks is investigated. The new and useful results obtained in this paper generalize and improve the corresponding results of recent works.

Suggested Citation

  • Lan, Heng-you & Cui, Yi-Shun, 2009. "A neural network method for solving a system of linear variational inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1245-1252.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1245-1252
    DOI: 10.1016/j.chaos.2008.05.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908002452
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.05.003?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. Abdel-Halim Hassan, I.H., 2008. "Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 53-65.
    2. Yucel, Eylem & Arik, Sabri, 2009. "Novel results for global robust stability of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1604-1614.
    3. Ding, Ke & Huang, Nan-Jing, 2008. "A new class of interval projection neural networks for solving interval quadratic program," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 718-725.
    4. Zhao, Weirui & Yan, Anzhi, 2009. "Stability analysis of neural networks with both variable and unbounded delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 697-707.
    5. Zhou, Qinghua & Wan, Li & Sun, Jianhua, 2007. "Exponential stability of reaction–diffusion generalized Cohen–Grossberg neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1713-1719.
    6. Cui, Shihua & Zhao, Tao & Guo, Jie, 2009. "Global robust exponential stability for interval neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1567-1576.
    7. Gao, Ming & Cui, Baotong, 2009. "Robust exponential stability of interval Cohen–Grossberg neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1914-1928.
    8. Chu, Tianguang & Yang, Haifeng, 2007. "A note on exponential convergence of neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1538-1545.
    9. 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.
    10. Zhao, Hongyong & Ding, Nan & Chen, Ling, 2009. "Almost sure exponential stability of stochastic fuzzy cellular neural networks with delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1653-1659.
    11. Momani, Shaher & Odibat, Zaid, 2007. "Numerical comparison of methods for solving linear differential equations of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1248-1255.
    12. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2005. "New stability conditions for neural networks with constant and variable delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1391-1398.
    13. Zhou, Qiyuan & Xiao, Bing & Yu, Yuehua & Peng, Lequn, 2007. "Existence and exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 860-866.
    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. Kashkynbayev, Ardak & Cao, Jinde & Suragan, Durvudkhan, 2021. "Global Lagrange stability analysis of retarded SICNNs," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Bao, Gang & Zeng, Zhigang, 2021. "Prescribed convergence analysis of recurrent neural networks with parameter variations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 858-870.
    3. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    4. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2009. "Exponential stability for nonautonomous neural networks with variable delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1152-1157.
    5. Sheng, Li & Yang, Huizhong, 2009. "Robust stability of uncertain Markovian jumping Cohen–Grossberg neural networks with mixed time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2120-2128.
    6. 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.
    7. Xu, Lan, 2009. "The variational iteration method for fourth order boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1386-1394.
    8. Roman Parovik, 2020. "Mathematical Modeling of Linear Fractional Oscillators," Mathematics, MDPI, vol. 8(11), pages 1-26, October.
    9. 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.
    10. Deng, Hongmin & Li, Tao & Wang, Qionghua & Li, Hongbin, 2009. "A fractional-order hyperchaotic system and its synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 962-969.
    11. Wang, Linshan & Zhang, Yan & Zhang, Zhe & Wang, Yangfan, 2009. "LMI-based approach for global exponential robust stability for reaction–diffusion uncertain neural networks with time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 900-905.
    12. Gui, Zhanji & Ge, Weigao, 2007. "Periodic solutions of nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1760-1771.
    13. Peng, Dezhong & Xiang, Yong & Yi, Zhang, 2009. "A new adaptive blind channel identification algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 354-359.
    14. Ammar, E.E., 2009. "On fuzzy random multiobjective quadratic programming," European Journal of Operational Research, Elsevier, vol. 193(2), pages 329-341, March.
    15. Odibat, Zaid M., 2009. "Exact solitary solutions for variants of the KdV equations with fractional time derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1264-1270.
    16. Marwan Abukhaled, 2013. "Variational Iteration Method for Nonlinear Singular Two-Point Boundary Value Problems Arising in Human Physiology," Journal of Mathematics, Hindawi, vol. 2013, pages 1-4, February.
    17. Mossa Al-sawalha, M. & Noorani, M.S.M., 2009. "A numeric–analytic method for approximating the chaotic Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1784-1791.
    18. Soliman, A.A., 2009. "On the solution of two-dimensional coupled Burgers’ equations by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1146-1155.
    19. Tuan Hoang, Manh & Nagy, A.M., 2019. "Uniform asymptotic stability of a Logistic model with feedback control of fractional order and nonstandard finite difference schemes," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 24-34.
    20. Zhang, Qiang & Xu, Xiaopeng Wei Jin, 2007. "Delay-dependent global stability results for delayed Hopfield neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 662-668.

    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:41:y:2009:i:3:p:1245-1252. 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.