IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v36y2008i5p1315-1319.html
   My bibliography  Save this article

Analysis of a 3D chaotic system

Author

Listed:
  • Tigan, Gheorghe
  • Opriş, Dumitru

Abstract

A 3D nonlinear chaotic system, called the T system, is analyzed in this paper. Horseshoe chaos is investigated via the heteroclinic Shilnikov method constructing a heteroclinic connection between the saddle equilibrium points of the system. Partially numerical computations are carried out to support the analytical results.

Suggested Citation

  • Tigan, Gheorghe & Opriş, Dumitru, 2008. "Analysis of a 3D chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1315-1319.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:5:p:1315-1319
    DOI: 10.1016/j.chaos.2006.07.052
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906007958
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.07.052?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. 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.
    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. Li, Xian-Feng & Chu, Yan-Dong & Zhang, Jian-Gang & Chang, Ying-Xiang, 2009. "Nonlinear dynamics and circuit implementation for a new Lorenz-like attractor," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2360-2370.
    2. Li, Xian-Feng & Chu, Yan-Dong & Leung, Andrew Y.T. & Zhang, Hui, 2017. "Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 24-30.
    3. Wu, Ranchao & Fang, Tianbao, 2015. "Stability and Hopf bifurcation of a Lorenz-like system," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 335-343.
    4. Yang, Shuangling & Qu, Jingjia, 2021. "On first integrals of a family of generalized Lorenz-like systems," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    5. Leonov, G.A. & Kuznetsov, N.V., 2015. "On differences and similarities in the analysis of Lorenz, Chen, and Lu systems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 334-343.
    6. Tigan, Gheorghe & Constantinescu, Dana, 2009. "Heteroclinic orbits in the T and the Lü systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 20-23.
    7. Wu, Yue & Zhou, Xiaobing & Chen, Jia & Hui, Bei, 2009. "Chaos synchronization of a new 3D chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1812-1819.
    8. Loong Soon Tee & Zabidin Salleh, 2013. "Dynamical Analysis of a Modified Lorenz System," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, December.
    9. Assali, El Abed, 2021. "Predefined-time synchronization of chaotic systems with different dimensions and applications," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

    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, 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.
    2. 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.
    3. Zhiqin Qiao & Xianyi Li, 2014. "Dynamical analysis and numerical simulation of a new Lorenz-type chaotic system," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 20(3), pages 264-283, May.
    4. 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.
    5. Arroyo, David & Li, Chengqing & Li, Shujun & Alvarez, Gonzalo, 2009. "Cryptanalysis of a computer cryptography scheme based on a filter bank," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 410-413.
    6. 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.
    7. Persohn, K.J. & Povinelli, R.J., 2012. "Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 238-245.

    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:36:y:2008:i:5:p:1315-1319. 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.