IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i2p783-794.html
   My bibliography  Save this article

On the chaotic synchronization of Lorenz systems with time-varying lags

Author

Listed:
  • Li, Lixiang
  • Peng, Haipeng
  • Yang, Yixian
  • Wang, Xiangdong

Abstract

Based on the stability theory of time-delay systems, the synchronization problem of chaotic systems with time-varying lags is discussed. Through the analysis of the error dynamical systems, the time-delay correlative synchronization controller is designed to achieve chaos synchronization. Finally, numerical simulations are provided to verify the effectiveness and feasibility of the developed method.

Suggested Citation

  • Li, Lixiang & Peng, Haipeng & Yang, Yixian & Wang, Xiangdong, 2009. "On the chaotic synchronization of Lorenz systems with time-varying lags," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 783-794.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:2:p:783-794
    DOI: 10.1016/j.chaos.2008.03.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908001501
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.03.014?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. Zhang, Gang & Liu, Zengrong & Ma, Zhongjun, 2007. "Generalized synchronization of different dimensional chaotic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 773-779.
    2. Shahverdiev, E.M. & Nuriev, R.A. & Hashimov, R.H. & Shore, K.A., 2006. "Chaos synchronization between the Mackey–Glass systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 854-861.
    3. Sarasola, C. & Torrealdea, F.J. & d’Anjou, A. & Graña, M., 2002. "Cost of synchronizing different chaotic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(4), pages 309-327.
    4. Zhang, Xiaohong & Liao, Xiaofeng & Li, Chuandong, 2005. "Impulsive control, complete and lag synchronization of unified chaotic system with continuous periodic switch," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 845-854.
    5. Sun, Zhongkui & Xu, Wei & Yang, Xiaoli & Fang, Tong, 2007. "Effects of time delays on bifurcation and chaos in a non-autonomous system with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 39-53.
    6. Yu, Wenwu & Cao, Jinde, 2007. "Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 467-482.
    7. Álvarez, G. & Li, Shujun & Montoya, F. & Pastor, G. & Romera, M., 2005. "Breaking projective chaos synchronization secure communication using filtering and generalized synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 775-783.
    8. Aguilar-López, Ricardo & Martinez-Guerra, Rafael, 2007. "Partial synchronization of different chaotic oscillators using robust PID feedback," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 572-581.
    9. Li, Chuandong & Liao, Xiaofeng & Zhang, Rong, 2005. "A unified approach for impulsive lag synchronization of chaotic systems with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1177-1184.
    10. Yassen, M.T., 2005. "Controlling chaos and synchronization for new chaotic system using linear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 913-920.
    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. An, Xin-Lei & Yu, Jian-Ning & Chu, Yan-Dong & Zhang, Jian-Gang & Zhang, Li, 2009. "Global chaos synchronization of three coupled nonlinear autonomous systems and a novel method of chaos encryption," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 865-873.
    2. Yassen, M.T., 2008. "Synchronization hyperchaos of hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 465-475.
    3. Zheng, Yongai & Chen, Guanrong, 2009. "Fuzzy impulsive control of chaotic systems based on TS fuzzy model," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 2002-2011.
    4. El-Dessoky, M.M., 2009. "Synchronization and anti-synchronization of a hyperchaotic Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1790-1797.
    5. Chu, Yan-Dong & Chang, Ying-Xiang & Zhang, Jian-Gang & Li, Xian-Feng & An, Xin-Lei, 2009. "Full state hybrid projective synchronization in hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1502-1510.
    6. Yu, Yongguang, 2008. "Adaptive synchronization of a unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 329-333.
    7. Ge, Zheng-Ming & Chang, Ching-Ming & Chen, Yen-Sheng, 2006. "Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1298-1315.
    8. Zhao, Yang, 2009. "Synchronization of two coupled systems of J-J type using active sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3035-3041.
    9. Márquez-Martínez, L.A. & Cuesta-García, J.R. & Pena Ramirez, J., 2022. "Boosting synchronization in chaotic systems: Combining past and present interactions," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. J. Humberto Pérez-Cruz & Pedro A. Tamayo-Meza & Maricela Figueroa & Ramón Silva-Ortigoza & Mario Ponce-Silva & R. Rivera-Blas & Mario Aldape-Pérez, 2019. "Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control," Complexity, Hindawi, vol. 2019, pages 1-10, July.
    11. Wu, Xiaoqun & Wang, Jinjun & Lu, Jun-an & Iu, Herbert H.C., 2007. "Hyperchaotic behavior in a non-autonomous unified chaotic system with continuous periodic switch," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1485-1490.
    12. Hoang, Thang Manh, 2011. "Complex synchronization manifold in coupled time-delayed systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 48-57.
    13. Mahmoud, Emad E. & Abo-Dahab, S.M., 2018. "Dynamical properties and complex anti synchronization with applications to secure communications for a novel chaotic complex nonlinear model," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 273-284.
    14. Sun, Mei & Tian, Lixin & Jiang, Shumin & Xu, Jun, 2007. "Feedback control and adaptive control of the energy resource chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1725-1734.
    15. Leung, Andrew Y.T. & Li, Xian-Feng & Chu, Yan-Dong & Rao, Xiao-Bo, 2015. "A simple adaptive-feedback scheme for identical synchronizing chaotic systems with uncertain parameters," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 172-183.
    16. Zhang, Ting & Wang, Jiang & Fei, Xiangyang & Deng, Bin, 2007. "Synchronization of coupled FitzHugh–Nagumo systems via MIMO feedback linearization control," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 194-202.
    17. Tang, Yinggan & Guan, Xinping, 2009. "Parameter estimation for time-delay chaotic system by particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1391-1398.
    18. Liu, Yong & Ren, Guodong & Zhou, Ping & Hayat, Tasawar & Ma, Jun, 2019. "Synchronization in networks of initially independent dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 370-380.
    19. Zaher, Ashraf A., 2009. "An improved chaos-based secure communication technique using a novel encryption function with an embedded cipher key," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2804-2814.
    20. Shahverdiev, E.M. & Hashimova, L.H. & Hashimova, N.T., 2008. "Chaos synchronization in some power systems," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 827-834.

    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:2:p:783-794. 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.