IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v387y2008i19p4947-4958.html
   My bibliography  Save this article

Dynamical behavior and influence of stochastic noise on certain generalized Boolean networks

Author

Listed:
  • Beck, Gary L.
  • Matache, Mihaela T.

Abstract

This study considers a simple Boolean network with N nodes, each node’s state at time t being determined by a certain number of parent nodes. The network is analyzed when the connectivity k is fixed or variable. Making use of a Boolean rule that is a generalization of Rule 22 of elementary cellular automata, a generalized formula for providing the probability of finding a node in state 1 at time t is determined. We show typical behaviors of the iterations, and we study the dynamics of the network through Lyapunov exponents, bifurcation diagrams and fixed point analysis. We conclude that the network may exhibit stability or chaos, depending on the underlying parameters. In general high connectivity is associated with a convergence to zero of the probability of finding a node in state 1 at time t. We also study analytically and numerically the dynamics of the network under a stochastic noise procedure. We show that under a smaller probability of disturbing the nodes through the noise procedure the system tends to exhibit more nodes in the same state. For many parameter combinations there is no critical value of the noise parameter below which the network remains organized and above which it behaves randomly.

Suggested Citation

  • Beck, Gary L. & Matache, Mihaela T., 2008. "Dynamical behavior and influence of stochastic noise on certain generalized Boolean networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4947-4958.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:19:p:4947-4958
    DOI: 10.1016/j.physa.2008.04.032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437108004044
    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.2008.04.032?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. Goodrich, Christopher S. & Matache, Mihaela T., 2007. "The stabilizing effect of noise on the dynamics of a Boolean network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 334-356.
    2. Fan, Jin & Li, Xiang & Fan Wang, Xiao, 2005. "On synchronous preference of complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 657-666.
    3. Marr, Carsten & Hütt, Marc-Thorsten, 2005. "Topology regulates pattern formation capacity of binary cellular automata on graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 641-662.
    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. Hung, Yao-Chen & Lin, Chai-Yu, 2014. "Modeling intrinsic noise in random Boolean networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 121-127.

    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. Goodrich, Christopher S. & Matache, Mihaela T., 2007. "The stabilizing effect of noise on the dynamics of a Boolean network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 334-356.
    2. Liu, Xian & Wang, Jinzhi & Huang, Lin, 2007. "Global synchronization for a class of dynamical complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 543-556.
    3. Liu, Xian & Wang, Jinzhi & Huang, Lin, 2007. "Stabilization of a class of dynamical complex networks based on decentralized control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 733-744.
    4. Liu, Meng & Shao, Yingying & Fu, Xinchu, 2009. "Complete synchronization on multi-layer center dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2584-2591.
    5. Malarz, Krzysztof & Kułakowski, Krzysztof, 2021. "Heider balance of a chain of actors as dependent on the interaction range and a thermal noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    6. Wu, Jianshe & Jiao, Licheng, 2007. "Observer-based synchronization in complex dynamical networks with nonsymmetric coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 469-480.
    7. Carvunis, Anne-Ruxandra & Latapy, Matthieu & Lesne, Annick & Magnien, Clémence & Pezard, Laurent, 2006. "Dynamics of three-state excitable units on Poisson vs. power-law random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 595-612.

    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:387:y:2008:i:19:p:4947-4958. 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: 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.