IDEAS home Printed from https://ideas.repec.org/a/taf/nmcmxx/v20y2014i3p264-283.html
   My bibliography  Save this article

Dynamical analysis and numerical simulation of a new Lorenz-type chaotic system

Author

Listed:
  • Zhiqin Qiao
  • Xianyi Li

Abstract

In this paper, a new 3D autonomous Lorenz-type chaotic system is modelled based on the condition that the system may generate chaos whereas it has only stable or non-hyperbolic equilibrium points. This system also includes some well-known Lorenz-like systems as its special cases, such as the diffusionless Lorenz system, the Burke-Shaw system and some other systems found. Although the new chaotic system is similar to other Lorenz-type systems in algebraic structure, they are topologically non-equivalent. This interesting fact motivates one to further investigate its dynamical behaviours, such as the number and the stability of equilibrium points, Hopf bifurcation and its direction, Poincaré maps, Lyapunov exponents and dissipativity, etc. Given numerical simulations not only verify the corresponding theoretically analytical results, but also demonstrate that this system possesses abundant and complex dynamical properties, which need further attention.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:nmcmxx:v:20:y:2014:i:3:p:264-283
    DOI: 10.1080/13873954.2013.824902
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/13873954.2013.824902
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/13873954.2013.824902?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.
    2. Huang, Kuifei & Yang, Qigui, 2009. "Stability and Hopf bifurcation analysis of a new system," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 567-578.
    3. Čelikovský, Sergej & Chen, Guanrong, 2005. "On the generalized Lorenz canonical form," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1271-1276.
    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. Wu, Jiening & Wang, Lidan & Chen, Guanrong & Duan, Shukai, 2016. "A memristive chaotic system with heart-shaped attractors and its implementation," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 20-29.
    2. Bazán Navarro, Ciro Eduardo & Benazic Tomé, Renato Mario, 2024. "Qualitative behavior in a fractional order IS-LM-AS macroeconomic model with stability analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 425-443.
    3. Wang, Haijun & Li, Xianyi, 2018. "A note on “Hopf bifurcation analysis and ultimate bound estimation of a new 4-D quadratic autonomous hyper-chaotic system” in [Appl. Math. Comput. 291 (2016) 323–339] by Amin Zarei and Saeed Tavakoli," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 1-4.

    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. Gao, Tiegang & Chen, Zengqiang & Gu, Qiaolun & Yuan, Zhuzhi, 2008. "A new hyper-chaos generated from generalized Lorenz system via nonlinear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 390-397.
    2. Meng Liu & Zhaoyan Wu & Xinchu Fu, 2022. "Dynamical Analysis of a One- and Two-Scroll Chaotic System," Mathematics, MDPI, vol. 10(24), pages 1-14, December.
    3. Doungmo Goufo, Emile Franc, 2017. "Solvability of chaotic fractional systems with 3D four-scroll attractors," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 443-451.
    4. 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.
    5. Li, Damei & Wu, Xiaoqun & Lu, Jun-an, 2009. "Estimating the ultimate bound and positively invariant set for the hyperchaotic Lorenz–Haken system," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1290-1296.
    6. Mathale, D. & Doungmo Goufo, Emile F. & Khumalo, M., 2020. "Coexistence of multi-scroll chaotic attractors for fractional systems with exponential law and non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. 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.
    8. 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.
    9. Huang, Kuifei & Yang, Qigui, 2009. "Stability and Hopf bifurcation analysis of a new system," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 567-578.
    10. Liao, Xiaoxin & Xu, F. & Wang, P. & Yu, Pei, 2009. "Chaos control and synchronization for a special generalized Lorenz canonical system – The SM system," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2491-2508.
    11. Zhou, Xiaobing & Wu, Yue & Li, Yi & Wei, Zhengxi, 2008. "Hopf bifurcation analysis of the Liu system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1385-1391.
    12. Wang, Xia, 2009. "Si’lnikov chaos and Hopf bifurcation analysis of Rucklidge system," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2208-2217.
    13. Qi, Guoyuan & Chen, Guanrong & Zhang, Yuhui, 2008. "On a new asymmetric chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 409-423.
    14. Qi, Guoyuan & van Wyk, Barend Jacobus & van Wyk, Michaël Antonie, 2009. "A four-wing attractor and its analysis," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2016-2030.
    15. Sun, Fengyun & Zhao, Yi & Zhou, Tianshou, 2007. "Identify fully uncertain parameters and design controllers based on synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1677-1682.
    16. 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.
    17. Xiong, Xiaohua & Wang, Junwei, 2009. "Conjugate Lorenz-type chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 923-929.
    18. 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.
    19. Yu, Simin & Tang, Wallace K.S., 2009. "Tetrapterous butterfly attractors in modified Lorenz systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1740-1749.
    20. Jiang, Yongxin & Sun, Jianhua, 2007. "Si’lnikov homoclinic orbits in a new chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 150-159.

    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:taf:nmcmxx:v:20:y:2014:i:3:p:264-283. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/NMCM20 .

    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.