IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v338y2004i3p367-378.html
   My bibliography  Save this article

Transition to chaos in complex dynamical networks

Author

Listed:
  • Li, Xiang
  • Chen, Guanrong
  • Ko, King-Tim

Abstract

The transition from a non-chaotic state to a chaotic state is a commonly concerned issue in the study of coupled dynamical networks. In this work, we consider a network consisting of nodes that are in non-chaotic states with parameters in non-chaotic regions before they are coupled together. We show that if these non-chaotic nodes are linked together through a suitable structural topology, positive Lyapunov exponents of the coupled network can be generated by choosing a certain uniform coupling strength, and the threshold for this coupling strength is determined by the complexity of the network topology. Moreover, we show that topological effects of scale-free and random networks, which are two basic types of complex network models, can be visualized based on their topological sensitivity to random failures and intentional attacks. Our simulation results on a 1000-node scale-free network and a 1000-node random network of the Logistic maps have verified that, during the transition from non-chaotic to chaotic states, if the topology is more heterogenous then the coupling strength required to achieve the transition can be decreased.

Suggested Citation

  • Li, Xiang & Chen, Guanrong & Ko, King-Tim, 2004. "Transition to chaos in complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 367-378.
    • Handle: RePEc:eee:phsmap:v:338:y:2004:i:3:p:367-378
    DOI: 10.1016/j.physa.2004.02.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437104002067
    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.2004.02.010?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. Li, Lixiang & Li, Weiwei & Kurths, Jürgen & Luo, Qun & Yang, Yixian & Li, Shudong, 2015. "Pinning adaptive synchronization of a class of uncertain complex dynamical networks with multi-link against network deterioration," Chaos, Solitons & Fractals, Elsevier, vol. 72(C), pages 20-34.
    2. repec:ctc:serie1:def14 is not listed on IDEAS
    3. Zhang, Hai-Feng & Wu, Rui-Xin & Fu, Xin-Chu, 2006. "The emergence of chaos in complex dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 472-479.
    4. Nicolò Pecora & Alessandro Spelta, 2014. "Shareholding Network in the Euro Area Banking Market," DISCE - Working Papers del Dipartimento di Economia e Finanza def014, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).
    5. Liu, Z.X. & Chen, Z.Q. & Yuan, Z.Z., 2007. "Pinning control of weighted general complex dynamical networks with time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 345-354.
    6. Yuan, Wu-Jie & Luo, Xiao-Shu & Jiang, Pin-Qun & Wang, Bing-Hong & Fang, Jin-Qing, 2008. "Transition to chaos in small-world dynamical network," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 799-806.

    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:338:y:2004:i:3:p:367-378. 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.