IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i5p2858-2864.html
   My bibliography  Save this article

Chaotic synchronization of two complex nonlinear oscillators

Author

Listed:
  • Mahmoud, Gamal M.
  • Mahmoud, Emad E.
  • Farghaly, Ahmed A.
  • Aly, Shaban A.

Abstract

Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing’s oscillators. Physica A 2001;292:193–206], a system of periodically forced complex Duffing’s oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schrödinger equation has also been pointed out.

Suggested Citation

  • Mahmoud, Gamal M. & Mahmoud, Emad E. & Farghaly, Ahmed A. & Aly, Shaban A., 2009. "Chaotic synchronization of two complex nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2858-2864.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2858-2864
    DOI: 10.1016/j.chaos.2009.04.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077909003658
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2009.04.027?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. 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.
    2. Park, Ju H., 2005. "Chaos synchronization of a chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 579-584.
    3. Park, Ju H., 2005. "On synchronization of unified chaotic systems via nonlinear Control," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 699-704.
    4. M. Mahmoud, Gamal & A. Mohamed, Ahmed & A. Aly, Shaban, 2001. "Strange attractors and chaos control in periodically forced complex Duffing's oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 292(1), pages 193-206.
    5. Jayaram, A. & Tadi, M., 2006. "Synchronization of chaotic systems based on SDRE method," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 707-715.
    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. 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.
    2. Sun, Yeong-Jeu, 2009. "Exponential synchronization between two classes of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2363-2368.
    3. Yu, Yongguang, 2008. "Adaptive synchronization of a unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 329-333.
    4. Guo, C.X. & Jiang, Q.Y. & Cao, Y.J., 2007. "Controlling chaotic oscillations via nonlinear observer approach," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 1014-1019.
    5. Vadivel, R. & Sabarathinam, S. & Wu, Yongbao & Chaisena, Kantapon & Gunasekaran, Nallappan, 2022. "New results on T–S fuzzy sampled-data stabilization for switched chaotic systems with its applications," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Park, Ju H., 2006. "Chaos synchronization of nonlinear Bloch equations," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 357-361.
    7. Huang, Cheng-Sea & Lian, Kuang-Yow & Su, Chien-Hsing & Wu, Jinn-Wen, 2008. "Stabilization at almost arbitrary points for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 452-459.
    8. Lam, H.K., 2009. "Output-feedback synchronization of chaotic systems based on sum-of-squares approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2624-2629.
    9. Yang, Li-Xin & Chu, Yan-Dong & Zhang, Jian-Gang & Li, Xian-Feng & Chang, Ying-Xiang, 2009. "Chaos synchronization in autonomous chaotic system via hybrid feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 214-223.
    10. Tarai (Poria), Anindita & Poria, Swarup & Chatterjee, Prasanta, 2009. "Synchronization of generalised linearly bidirectionally coupled unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 885-892.
    11. Yao, Qijia, 2021. "Synchronization of second-order chaotic systems with uncertainties and disturbances using fixed-time adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    12. Baishya, Chandrali & Premakumari, R.N. & Samei, Mohammad Esmael & Naik, Manisha Krishna, 2023. "Chaos control of fractional order nonlinear Bloch equation by utilizing sliding mode controller," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    13. Mossa Al-sawalha, M. & Noorani, M.S.M., 2009. "On anti-synchronization of chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 170-179.
    14. Ahmadi, Ali Akbar & Majd, Vahid Johari, 2009. "Robust synchronization of a class of uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1092-1096.
    15. Zhou, Shuang-Shuang & Jahanshahi, Hadi & Din, Qamar & Bekiros, Stelios & Alcaraz, Raúl & Alassafi, Madini O. & Alsaadi, Fawaz E. & Chu, Yu-Ming, 2021. "Discrete-time macroeconomic system: Bifurcation analysis and synchronization using fuzzy-based activation feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    16. 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.
    17. 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.
    18. Sharma, B.B. & Kar, I.N., 2009. "Parametric convergence and control of chaotic system using adaptive feedback linearization," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1475-1483.
    19. Gao, Xin & Yu, Juebang, 2005. "Chaos in the fractional order periodically forced complex Duffing’s oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1097-1104.
    20. Lazaro M Sanchez-Rodriguez & Yasser Iturria-Medina & Erica A Baines & Sabela C Mallo & Mehdy Dousty & Roberto C Sotero & on behalf of The Alzheimer’s Disease Neuroimaging Initiative, 2018. "Design of optimal nonlinear network controllers for Alzheimer's disease," PLOS Computational Biology, Public Library of Science, vol. 14(5), pages 1-24, May.

    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:42:y:2009:i:5:p:2858-2864. 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.