IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v32y2007i5p1823-1829.html
   My bibliography  Save this article

Synchronization of two chaotic four-dimensional systems using active control

Author

Listed:
  • Lei, Youming
  • Xu, Wei
  • Xie, Wenxian

Abstract

In this paper, we introduce an active control to synchronize two identical chaotic 4D systems presented by Qi et al. recently. Based on Routh–Hurwitz criteria, a nonlinear controller and some generic sufficient conditions for global asymptotic synchronization are obtained. Numerical simulations demonstrate the validity and feasibility of the proposed method.

Suggested Citation

  • Lei, Youming & Xu, Wei & Xie, Wenxian, 2007. "Synchronization of two chaotic four-dimensional systems using active control," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1823-1829.
  • Handle: RePEc:eee:chsofr:v:32:y:2007:i:5:p:1823-1829
    DOI: 10.1016/j.chaos.2005.12.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905012208
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2005.12.014?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. Bernd Blasius & Amit Huppert & Lewi Stone, 1999. "Complex dynamics and phase synchronization in spatially extended ecological systems," Nature, Nature, vol. 399(6734), pages 354-359, May.
    2. Qi, Guoyuan & Du, Shengzhi & Chen, Guanrong & Chen, Zengqiang & yuan, Zhuzhi, 2005. "On a four-dimensional chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1671-1682.
    3. Chen, Hsien-Keng, 2005. "Global chaos synchronization of new chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1245-1251.
    4. Lei, Youming & Xu, Wei & Shen, Jianwei & Fang, Tong, 2006. "Global synchronization of two parametrically excited systems using active control," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 428-436.
    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. J. Humberto Pérez-Cruz, 2018. "Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control," Complexity, Hindawi, vol. 2018, pages 1-19, December.
    2. Du, Shengzhi & van Wyk, Barend J. & Qi, Guoyuan & Tu, Chunling, 2009. "Chaotic system synchronization with an unknown master model using a hybrid HOD active control approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1900-1913.
    3. Upadhyay, Ranjit Kumar & Rai, Vikas, 2009. "Complex dynamics and synchronization in two non-identical chaotic ecological systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2233-2241.
    4. 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.

    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. Lei, Youming & Xu, Wei & Shen, Jianwei, 2007. "Robust synchronization of chaotic non-autonomous systems using adaptive-feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 371-379.
    2. Chen, Hsien-Keng, 2005. "Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lü," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1049-1056.
    3. Mahmoud, Gamal M. & Aly, Shaban A. & Farghaly, Ahmed A., 2007. "On chaos synchronization of a complex two coupled dynamos system," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 178-187.
    4. Agiza, H.N. & Matouk, A.E., 2006. "Adaptive synchronization of Chua’s circuits with fully unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 219-227.
    5. Lei, Youming & Xu, Wei & Shen, Jianwei & Fang, Tong, 2006. "Global synchronization of two parametrically excited systems using active control," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 428-436.
    6. Wu, Cunli & Fang, Tong & Rong, Haiwu, 2007. "Chaos synchronization of two stochastic Duffing oscillators by feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1201-1207.
    7. Ge, Zheng-Ming & Chang, Ching-Ming, 2009. "Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1959-1974.
    8. Pal, Pikaso & Mukherjee, V. & Alemayehu, Hinsermu & Jin, Gang Gyoo & Feyisa, Gosa, 2021. "Generalized adaptive backstepping sliding mode control for synchronizing chaotic systems with uncertainties and disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 793-807.
    9. 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.
    10. Sun, Yeong-Jeu, 2009. "An exponential observer for the generalized Rossler chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2457-2461.
    11. Tam, Lap Mou & Si Tou, Wai Meng, 2008. "Parametric study of the fractional-order Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 817-826.
    12. Barrio, Roberto, 2005. "Sensitivity tools vs. Poincaré sections," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 711-726.
    13. 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.
    14. Hoang, Thang Manh, 2011. "Complex synchronization manifold in coupled time-delayed systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 48-57.
    15. Singh, Piyush Pratap & Singh, Jay Prakash & Roy, B.K., 2014. "Synchronization and anti-synchronization of Lu and Bhalekar–Gejji chaotic systems using nonlinear active control," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 31-39.
    16. Suresh, R. & Senthilkumar, D.V. & Lakshmanan, M. & Kurths, J., 2016. "Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 235-245.
    17. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    18. Valenti, D. & Tranchina, L. & Brai, M. & Caruso, A. & Cosentino, C. & Spagnolo, B., 2008. "Environmental metal pollution considered as noise: Effects on the spatial distribution of benthic foraminifera in two coastal marine areas of Sicily (Southern Italy)," Ecological Modelling, Elsevier, vol. 213(3), pages 449-462.
    19. Park, Ju H., 2005. "Chaos synchronization of a chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 579-584.
    20. Chen, Zengqiang & Yang, Yong & Yuan, Zhuzhi, 2008. "A single three-wing or four-wing chaotic attractor generated from a three-dimensional smooth quadratic autonomous system," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1187-1196.

    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:32:y:2007:i:5:p:1823-1829. 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.