IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i5p1232-1245.html
   My bibliography  Save this article

Analysis on the evolution process of BFW-like model with discontinuous percolation of multiple giant components

Author

Listed:
  • Zhang, Renquan
  • Wei, Wei
  • Guo, Binghui
  • Zhang, Yang
  • Zheng, Zhiming

Abstract

Recently, the modified BFW model on random graphs [W. Chen, R.M. D’Souza, Phys. Rev. Lett. 106 (2011) 115701], which shows a discontinuous percolation transition with multiple giant components, has attracted much attention from physicists and statisticians. In this paper, by establishing the evolution equations on the modified BFW model, the evolution process and steady-states on both random graphs and finite-dimensional lattices are analyzed. On a random graph, by varying the edge accepted rate α, the system stabilizes in a steady-state with different numbers of giant components. Moreover, a close correspondence is built between the values of α and the number of giant components in steady-states, the efficiency of which is verified by the numerical simulations. Then, the sizes of giant components for different evolution strategies can be obtained by solving some constraints derived from the evolution equations. Meanwhile, a similar analysis is expanded to finite-dimensional lattices, and we find the BFW (α) model on a finite-dimensional lattice has different steady-states from those on a random graph, but they have the same evolution mechanism. The analysis of the evolution process and steady-state is of great help to explain the properties of discontinuous percolation and the role of nonlocality.

Suggested Citation

  • Zhang, Renquan & Wei, Wei & Guo, Binghui & Zhang, Yang & Zheng, Zhiming, 2013. "Analysis on the evolution process of BFW-like model with discontinuous percolation of multiple giant components," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1232-1245.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:5:p:1232-1245
    DOI: 10.1016/j.physa.2012.11.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112009983
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2012.11.033?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.

    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:phsmap:v:392:y:2013:i:5:p:1232-1245. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.