IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n781594.html

Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization

Author

Listed:
  • Jiezhi Wang
  • Qing Zhang
  • Zengqiang Chen
  • Hang Li

Abstract

Two ellipsoidal ultimate boundary regions of a special three‐dimensional (3D) chaotic system are proposed. To this chaotic system, the linear coefficient of the ith state variable in the ith state equation has the same sign; it also has two one‐order terms and one quadratic cross‐product term in each equation. A numerical solution and an analytical expression of the ultimate bounds are received. To get the analytical expression of the ultimate boundary region, a new result of one maximum optimization question is proved. The corresponding ultimate boundary regions are demonstrated through numerical simulations. Utilizing the bounds obtained, a linear controller is proposed to achieve the complete chaos synchronization. Numerical simulation exhibits the feasibility of the designed scheme.

Suggested Citation

  • Jiezhi Wang & Qing Zhang & Zengqiang Chen & Hang Li, 2014. "Ultimate Bound of a 3D Chaotic System and Its Application in Chaos Synchronization," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:781594
    DOI: 10.1155/2014/781594
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/781594
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/781594?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
    ---><---

    References listed on IDEAS

    as
    1. Shu, Yonglu & Xu, Hongxing & Zhao, Yunhong, 2009. "Estimating the ultimate bound and positively invariant set for a new chaotic system and its application in chaos synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2852-2857.
    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. Liang, Xiyin & Qi, Guoyuan, 2017. "Mechanical analysis of Chen chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 173-177.
    2. 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).
    3. 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.
    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. Lijuan Chen & Mingchu Yu & Jinnan Luo & Jinpeng Mi & Kaibo Shi & Song Tang, 2024. "Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity," Mathematics, MDPI, vol. 12(12), pages 1-17, June.
    6. 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 synchronization using optimized fractional order sli," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    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. Zhang Jiangang & Chu Yandong & Du Wenju & Chang Yingxiang & An Xinlei, 2014. "Hopf Bifurcation Analysis in a New Chaotic System with Chaos Entanglement Function," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    10. 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.
    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. Zhang, Enrui & Li, Xianyi, 2026. "Complex bifurcations and new types of structure uncovered in the Qi system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 244(C), pages 226-263.
    13. 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.
    14. 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.
    15. 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).
    16. Hou, Yi-You & Lin, Ming-Hung & Saberi-Nik, Hassan & Arya, Yogendra, 2024. "Boundary analysis and energy feedback control of fractional-order extended Malkus–Robbins dynamo system," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    17. Jian, Jigui & Wu, Kai & Wang, Baoxian, 2020. "Global Mittag-Leffler boundedness and synchronization for fractional-order chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    18. Huang, Jun & Han, Zhengzhi & Cai, Xiushan & Liu, Leipo, 2011. "Uniformly ultimately bounded tracking control of linear differential inclusions with stochastic disturbance," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(12), pages 2662-2672.
    19. 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).
    20. Loong Soon Tee & Zabidin Salleh, 2013. "Dynamical Analysis of a Modified Lorenz System," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, December.

    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:wly:jnlaaa:v:2014:y:2014:i:1:n:781594. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.