IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i5p2756-2761.html
   My bibliography  Save this article

A computer-assisted proof for the existence of horseshoe in a novel chaotic system

Author

Listed:
  • Wu, Wen-Juan
  • Chen, Zeng-Qiang
  • Yuan, Zhu-Zhi

Abstract

The dynamics of a novel chaotic system are studied, and a rigorous computer-assisted proof for existence of horseshoe in this system is given. A Poincaré section is properly chosen to obtain the Poincaré map, which is proved to be semi-conjugate to the 4-shift map by utilizing topological horseshoe theory. This implies the entropy of the system is no less than log 4, and the system definitely exhibits chaos.

Suggested Citation

  • Wu, Wen-Juan & Chen, Zeng-Qiang & Yuan, Zhu-Zhi, 2009. "A computer-assisted proof for the existence of horseshoe in a novel chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2756-2761.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2756-2761
    DOI: 10.1016/j.chaos.2008.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908004748
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.10.008?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. Wu, Wenjuan & Chen, Zengqiang & Yuan, Zhuzhi, 2009. "The evolution of a novel four-dimensional autonomous system: Among 3-torus, limit cycle, 2-torus, chaos and hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2340-2356.
    2. Qi, Guoyuan & Chen, Guanrong & Du, Shengzhi & Chen, Zengqiang & Yuan, Zhuzhi, 2005. "Analysis of a new chaotic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 295-308.
    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. Xin, Baogui & Ma, Junhai & Gao, Qin, 2009. "The complexity of an investment competition dynamical model with imperfect information in a security market," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2425-2438.
    2. Liang, Xiyin & Qi, Guoyuan, 2017. "Mechanical analysis of Chen chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 173-177.
    3. Dong, Chengwei & Yang, Min & Jia, Lian & Li, Zirun, 2024. "Dynamics investigation and chaos-based application of a novel no-equilibrium system with coexisting hidden attractors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    4. Ghamati, Mina & Balochian, Saeed, 2015. "Design of adaptive sliding mode control for synchronization Genesio–Tesi chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 111-117.
    5. 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).
    6. Du Mingjing & Yulan Wang, 2019. "Some Novel Complex Dynamic Behaviors of a Class of Four-Dimensional Chaotic or Hyperchaotic Systems Based on a Meshless Collocation Method," Complexity, Hindawi, vol. 2019, pages 1-15, October.
    7. Qi, Guoyuan & van Wyk, Michaël Antonie & van Wyk, Barend Jacobus & Chen, Guanrong, 2009. "A new hyperchaotic system and its circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2544-2549.
    8. Guohui Li & Xiangyu Zhang & Hong Yang, 2019. "Numerical Analysis, Circuit Simulation, and Control Synchronization of Fractional-Order Unified Chaotic System," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    9. Singh, Jay Prakash & Roy, Binoy Krishna, 2018. "Five new 4-D autonomous conservative chaotic systems with various type of non-hyperbolic and lines of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 81-91.
    10. 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.
    11. Zhang, Jianxiong & Tang, Wansheng, 2009. "Analysis and control for a new chaotic system via piecewise linear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2181-2190.
    12. Daniel Ríos-Rivera & Alma Y. Alanis & Edgar N. Sanchez, 2020. "Neural-Impulsive Pinning Control for Complex Networks Based on V-Stability," Mathematics, MDPI, vol. 8(9), pages 1-20, August.
    13. Saifullah, Sayed & Ali, Amir & Franc Doungmo Goufo, Emile, 2021. "Investigation of complex behaviour of fractal fractional chaotic attractor with mittag-leffler Kernel," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    14. Dong, Chengwei & Liu, Huihui & Jie, Qi & Li, Hantao, 2022. "Topological classification of periodic orbits in the generalized Lorenz-type system with diverse symbolic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    15. Bi, Haiyun & Qi, Guoyuan & Hu, Jianbing & Faradja, Philippe & Chen, Guanrong, 2020. "Hidden and transient chaotic attractors in the attitude system of quadrotor unmanned aerial vehicle," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    16. Loong Soon Tee & Zabidin Salleh, 2013. "Dynamical Analysis of a Modified Lorenz System," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, December.
    17. Zhou, Leilei & Chen, Zengqiang & Wang, Zhonglin & Wang, Jiezhi, 2016. "On the analysis of local bifurcation and topological horseshoe of a new 4D hyper-chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 148-156.
    18. Alma Y. Alanis & Daniel Ríos-Rivera & Edgar N. Sanchez & Oscar D. Sanchez, 2021. "Learning Impulsive Pinning Control of Complex Networks," Mathematics, MDPI, vol. 9(19), pages 1-9, October.
    19. Megam Ngouonkadi, E.B. & Fotsin, H.B. & Louodop Fotso, P. & Kamdoum Tamba, V. & Cerdeira, Hilda A., 2016. "Bifurcations and multistability in the extended Hindmarsh–Rose neuronal oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 151-163.
    20. Çalış, Yasemin & Demirci, Ali & Özemir, Cihangir, 2022. "Hopf bifurcation of a financial dynamical system with delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 343-361.

    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:5:p:2756-2761. 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.