IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v155y2022ics0960077921010778.html
   My bibliography  Save this article

Constructing conditional symmetry in symmetric chaotic systems

Author

Listed:
  • Li, Chunbiao
  • Sprott, Julien Clinton
  • Zhang, Xin
  • Chai, Lin
  • Liu, Zuohua

Abstract

Based on the analysis of polarity balance and exhaustive computer searching, a series of symmetric chaotic flows is found for hosting conditional symmetry. Symmetric structure shapes the elegant symmetric phase trajectory, and conditional symmetry permits the convenience of embedding an extra set of coexisting symmetric attractors. Bifurcation analysis proves the coexistence of two independent processes of dynamical behavior under conditional symmetry. Circuit simulation confirms the numerical and theoretical analysis.

Suggested Citation

  • Li, Chunbiao & Sprott, Julien Clinton & Zhang, Xin & Chai, Lin & Liu, Zuohua, 2022. "Constructing conditional symmetry in symmetric chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010778
    DOI: 10.1016/j.chaos.2021.111723
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921010778
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111723?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. Bao, B.C. & Bao, H. & Wang, N. & Chen, M. & Xu, Q., 2017. "Hidden extreme multistability in memristive hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 102-111.
    2. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
    3. Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Kengne, Jacques & Jafari, Sajad & Pham, Viet-Thanh, 2018. "A new four-dimensional system containing chaotic or hyper-chaotic attractors with no equilibrium, a line of equilibria and unstable equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 108-118.
    4. 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.
    5. Munmuangsaen, Buncha & Srisuchinwong, Banlue, 2018. "A hidden chaotic attractor in the classical Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 61-66.
    6. Zhenyu Gu & Chunbiao Li & Herbert H. C. Iu & Fuhong Min & Yibo Zhao, 2019. "Constructing hyperchaotic attractors of conditional symmetry," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(10), pages 1-9, October.
    7. Sprott, J.C. & Munmuangsaen, Buncha, 2018. "Comment on “A hidden chaotic attractor in the classical Lorenz system”," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 261-262.
    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. Wang, Ning & Xu, Dan & Kuznetsov, N.V. & Bao, Han & Chen, Mo & Xu, Quan, 2023. "Experimental observation of hidden Chua’s attractor," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Zhenggang Guo & Junjie Wen & Jun Mou, 2022. "Dynamic Analysis and DSP Implementation of Memristor Chaotic Systems with Multiple Forms of Hidden Attractors," Mathematics, MDPI, vol. 11(1), pages 1-13, December.
    3. Chen, Yuanlin & Lu, Tianxiu & Wang, Qianxue, 2024. "The chaotic properties and circuit design of a generalized high-dimensional integer-domain system," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    4. Zhoubin Sheng & Chunbiao Li & Yikai Gao & Zhinan Li & Lin Chai, 2023. "A Switchable Chaotic Oscillator with Multiscale Amplitude/Frequency Control," Mathematics, MDPI, vol. 11(3), pages 1-11, January.
    5. Sivaganesh, G. & Srinivasan, K. & Fozin, T. Fonzin & Pradeep, R. Gladwin, 2023. "Emergence of chaotic hysteresis in a second-order non-autonomous chaotic circuit," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Wang, Zhen & Ahmadi, Atefeh & Tian, Huaigu & Jafari, Sajad & Chen, Guanrong, 2023. "Lower-dimensional simple chaotic systems with spectacular features," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    7. Zhang, Fangfang & Zhang, Shuaihu & Chen, Guanrong & Li, Chunbiao & Li, Zhengfeng & Pan, Changchun, 2022. "Special attractors and dynamic transport of the hybrid-order complex Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 164(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. Mezatio, Brice Anicet & Motchongom, Marceline Tingue & Wafo Tekam, Blaise Raoul & Kengne, Romanic & Tchitnga, Robert & Fomethe, Anaclet, 2019. "A novel memristive 6D hyperchaotic autonomous system with hidden extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 100-115.
    2. Liang, Bo & Hu, Chenyang & Tian, Zean & Wang, Qiao & Jian, Canling, 2023. "A 3D chaotic system with multi-transient behavior and its application in image encryption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    3. Lai, Qiang & Xu, Guanghui & Pei, Huiqin, 2019. "Analysis and control of multiple attractors in Sprott B system," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 192-200.
    4. Yu, Hui & Du, Shengzhi & Dong, Enzeng & Tong, Jigang, 2022. "Transient behaviors and equilibria-analysis-based boundary crisis analysis in a smooth 4D dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    5. Tchitnga, R. & Mezatio, B.A. & Fozin, T. Fonzin & Kengne, R. & Louodop Fotso, P.H. & Fomethe, A., 2019. "A novel hyperchaotic three-component oscillator operating at high frequency," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 166-180.
    6. Jia, Hongyan & Shi, Wenxin & Wang, Lei & Qi, Guoyuan, 2020. "Energy analysis of Sprott-A system and generation of a new Hamiltonian conservative chaotic system with coexisting hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    7. Wu, Qiujie & Hong, Qinghui & Liu, Xiaoyang & Wang, Xiaoping & Zeng, Zhigang, 2020. "A novel amplitude control method for constructing nested hidden multi-butterfly and multiscroll chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    8. Cang, Shijian & Wang, Luo & Zhang, Yapeng & Wang, Zenghui & Chen, Zengqiang, 2022. "Bifurcation and chaos in a smooth 3D dynamical system extended from Nosé-Hoover oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    9. Ahmad, Shabir & Ullah, Aman & Akgül, Ali, 2021. "Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Wang, Zhen & Ahmadi, Atefeh & Tian, Huaigu & Jafari, Sajad & Chen, Guanrong, 2023. "Lower-dimensional simple chaotic systems with spectacular features," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    11. Bao, B. & Peol, M.A. & Bao, H. & Chen, M. & Li, H. & Chen, B., 2021. "No-argument memristive hyper-jerk system and its coexisting chaotic bubbles boosted by initial conditions," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    12. Othman Abdullah Almatroud & Karthikeyan Rajagopal & Viet-Thanh Pham & Giuseppe Grassi, 2024. "A Novel Chaotic System with Only Quadratic Nonlinearities: Analysis of Dynamical Properties and Stability," Mathematics, MDPI, vol. 12(4), pages 1-10, February.
    13. Gritli, Hassène, 2019. "Poincaré maps design for the stabilization of limit cycles in non-autonomous nonlinear systems via time-piecewise-constant feedback controllers with application to the chaotic Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 127-145.
    14. Jafari, Sajad & Dehghan, Soroush & Chen, Guanrong & Kingni, Sifeu Takougang & Rajagopal, Karthikeyan, 2018. "Twin birds inside and outside the cage," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 135-140.
    15. Faradja, Philippe & Qi, Guoyuan, 2020. "Analysis of multistability, hidden chaos and transient chaos in brushless DC motor," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    16. Zhang, Sen & Zeng, Yicheng, 2019. "A simple Jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 25-40.
    17. Chen, Mo & Wang, Chao & Bao, Han & Ren, Xue & Bao, Bocheng & Xu, Quan, 2020. "Reconstitution for interpreting hidden dynamics with stable equilibrium point," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    18. Wang, Ran & Li, Chunbiao & Kong, Sixiao & Jiang, Yicheng & Lei, Tengfei, 2022. "A 3D memristive chaotic system with conditional symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    19. Wang, Zhen & Abdolmohammadi, Hamid Reza & Alsaadi, Fawaz E. & Hayat, Tasawar & Pham, Viet-Thanh, 2018. "A new oscillator with infinite coexisting asymmetric attractors," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 252-258.
    20. Peng, Xuenan & Zeng, Yicheng, 2020. "Image encryption application in a system for compounding self-excited and hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

    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:155:y:2022:i:c:s0960077921010778. 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.