IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v189y2024ip1s0960077924012360.html
   My bibliography  Save this article

Cyclic symmetric dynamics in chaotic maps

Author

Listed:
  • Liu, Jin
  • Sun, Kehui
  • Wang, Huihai

Abstract

In a recent paper (Liu et al., 2024), we reported on the microscopic mechanism underlying multistability in discrete dynamical systems, suggesting the potential for higher, even arbitrary-dimensional multistability in our conclusions. Before we can validate it, a fundamental question arises: what method can preserve the global dynamics of systems while allowing for an increase in dimensionality? This paper identifies the cyclic symmetric structure as a crucial solution and establishes two two-dimensional maps model based on it. The presence of multistability in any direction is affirmed, with this phenomenon representing either homogeneous or heterogeneous infinite expansion of the medium in multidimensional space. Furthermore, we uncover a range of dynamical characteristics, including grid-like phase trajectories, scale-free attractor clusters, fractal basin structures, symmetric attractors, and chaotic diffusion, all rooted in the system’s symmetric dynamical nature. This research not only enhances the comprehension of high-dimensional symmetric dynamics, but also offers a novel perspective for elucidating related models and phenomena.

Suggested Citation

  • Liu, Jin & Sun, Kehui & Wang, Huihai, 2024. "Cyclic symmetric dynamics in chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
  • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924012360
    DOI: 10.1016/j.chaos.2024.115684
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924012360
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2024.115684?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. Zhu, Wanting & Sun, Kehui & He, Shaobo & Wang, Huihai & Liu, Wenhao, 2023. "A class of m-dimension grid multi-cavity hyperchaotic maps and its application," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Tutueva, Aleksandra V. & Moysis, Lazaros & Rybin, Vyacheslav G. & Kopets, Ekaterina E. & Volos, Christos & Butusov, Denis N., 2022. "Fast synchronization of symmetric Hénon maps using adaptive symmetry control," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Rajagopal, Karthikeyan & Cimen, Murat Erhan & Jafari, Sajad & Singh, Jay Prakash & Roy, Binoy Krishna & Akmese, Omer Faruk & Akgul, Akif, 2021. "A family of circulant megastable chaotic oscillators, its application for the detection of a feeble signal and PID controller for time-delay systems by using chaotic SCA algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    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. Othman Abdullah Almatroud & Viet-Thanh Pham & Giuseppe Grassi & Mohammad Alshammari & Sahar Albosaily & Van Van Huynh, 2023. "Design of High-Dimensional Maps with Sine Terms," Mathematics, MDPI, vol. 11(17), pages 1-10, August.
    2. Tutueva, Aleksandra & Moysis, Lazaros & Rybin, Vyacheslav & Zubarev, Alexander & Volos, Christos & Butusov, Denis, 2022. "Adaptive symmetry control in secure communication systems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Murat Çimen, 2024. "Portfolio Optimization with Artificial Hummingbird Algorithm for Cement Industry," Istanbul Business Research, Istanbul University Business School, vol. 53(3), pages 351-378, December.
    4. Yao, Zhao & Sun, Kehui & He, Shaobo, 2024. "Energy variation rate synchronization for coupled chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    5. Zhu, Wanting & Sun, Kehui & Wang, Huihai & Fu, Longxiang & Minati, Ludovico, 2024. "Dynamics, synchronization and analog circuit implementation of a discrete neuron-like map with pulsating spiral dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    6. Ding, Jianpeng & Lei, Youming & Xie, Jianfei & Small, Michael, 2024. "Chaos synchronization of two coupled map lattice systems using safe reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    7. Zhang, Zefeng & Huang, Lilian & Liu, Jin & Guo, Qiang & Du, Xiuli, 2022. "A new method of constructing cyclic symmetric conservative chaotic systems and improved offset boosting control," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    8. Fan, Zhenyi & Zhang, Chenkai & Wang, Yiming & Du, Baoxiang, 2023. "Construction, dynamic analysis and DSP implementation of a novel 3D discrete memristive hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    9. Ostrovskii, Valerii Yu. & Rybin, Vyacheslav G. & Karimov, Artur I. & Butusov, Denis N., 2022. "Inducing multistability in discrete chaotic systems using numerical integration with variable symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    10. Fan, Zhenyi & Sun, Xu & Zhao, Jingjing & Zhang, Chenkai & Du, Baoxiang, 2024. "Dynamics analysis and feasibility verification of a 3D discrete memristive chaotic map with multi-vortex-like volume behavior," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    11. Cao, Hongli & Cao, Yinghong & Qin, Lei & Mou, Jun, 2025. "Dynamical analysis, multi-cavity control and DSP implementation of a novel memristive autapse neuron model emulating brain behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 191(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:189:y:2024:i:p1:s0960077924012360. 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.