IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v111y2018icp206-212.html
   My bibliography  Save this article

Analysis of global properties for dynamical systems by a modified digraph cell mapping method

Author

Listed:
  • Yue, Xiaole
  • Xu, Wei
  • Zhang, Ying
  • Du, Lin

Abstract

A modified procedure is proposed in this paper to solve the limitations of digraph cell mapping method in accurately analyzing the global properties of dynamical system, such as fractal basin boundaries. Firstly a rough cell structure is applied to the generalized cell mapping (GCM) method to obtain the general global properties of dynamical systems with digraph algorithm, and then a procedure based on the composite cell coordinate system method is proposed to increase the calculation accuracy. In order to further increase the calculation speed, a simple and feasible parallel strategy is applied during the creation process of one-step transition probability matrix for the GCM method. Meanwhile, the memory consumption can be greatly reduced by storing the one-step transition probability matrix as finite separate data files. The accurate global properties of two examples, a nonlinear oscillator with fractal basin structure and the Lorenz system, are demonstrated to show the effectiveness of our proposed improvement strategy.

Suggested Citation

  • Yue, Xiaole & Xu, Wei & Zhang, Ying & Du, Lin, 2018. "Analysis of global properties for dynamical systems by a modified digraph cell mapping method," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 206-212.
    • Handle: RePEc:eee:chsofr:v:111:y:2018:i:c:p:206-212
    DOI: 10.1016/j.chaos.2018.04.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007791830170X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.04.025?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ma, Shichao & Wang, Liang & Ning, Xin & Yue, Xiaole & Xu, Wei, 2019. "Probabilistic responses of three-dimensional stochastic vibro-impact systems," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 308-314.
    2. Yue, Xiaole & Xu, Yong & Xu, Wei & Sun, Jian-Qiao, 2019. "Probabilistic response of dynamical systems based on the global attractor with the compatible cell mapping method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 509-519.
    3. Hasin Md. Muhtasim Taqi & Humaira Nafisa Ahmed & Sumit Paul & Maryam Garshasbi & Syed Mithun Ali & Golam Kabir & Sanjoy Kumar Paul, 2020. "Strategies to Manage the Impacts of the COVID-19 Pandemic in the Supply Chain: Implications for Improving Economic and Social Sustainability," Sustainability, MDPI, vol. 12(22), pages 1-25, November.
    4. Yue, Xiaole & Lv, Ge & Zhang, Ying, 2021. "Rare and hidden attractors in a periodically forced Duffing system with absolute nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 150(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:111:y:2018:i:c:p:206-212. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.