IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v460y2016icp1-15.html
   My bibliography  Save this article

Unstable network fragmentation in co-evolution of Potts spins and system topology

Author

Listed:
  • Toruniewska, Joanna
  • Suchecki, Krzysztof
  • Hołyst, Janusz A.

Abstract

We investigate co-evolution of discrete q-state Potts model and the underlying network topology, where spin changes and link re-wiring follow the same canonical ensemble dynamics in a constant temperature. It means that there are no absorbing, frozen states present in our model. Depending on the temperature T and probability of link dynamics p the system can exist in one of three states: ordered, disordered and ordered clusters (fragmented network), with the last being unstable and slowly relaxing into ordered state. The transition from ordered clusters to globally ordered system is characterized by non-exponential, slow growth of the order parameter. We investigate this process analytically and explain the transition characteristics as the result of the dominance of activity of “surface” nodes in each ordered cluster, as opposed to “bulk” nodes that are inactive.

Suggested Citation

  • Toruniewska, Joanna & Suchecki, Krzysztof & Hołyst, Janusz A., 2016. "Unstable network fragmentation in co-evolution of Potts spins and system topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 1-15.
    • Handle: RePEc:eee:phsmap:v:460:y:2016:i:c:p:1-15
    DOI: 10.1016/j.physa.2016.04.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116301601
    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.2016.04.029?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. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
    2. Lambiotte, Renaud & González-Avella, Juan Carlos, 2011. "On co-evolution and the importance of initial conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 392-397.
    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. Yin, Likang & Deng, Yong, 2018. "Measuring transferring similarity via local information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 498(C), pages 102-115.
    2. Małgorzata J Krawczyk & Krzysztof Kułakowski & Janusz A Hołyst, 2018. "Hierarchical partitions of social networks between rivaling leaders," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-13, March.

    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. Ya-Chun Gao & Zong-Wen Wei & Bing-Hong Wang, 2013. "Dynamic Evolution Of Financial Network And Its Relation To Economic Crises," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 1-10.
    2. Wang, Qingyun & Duan, Zhisheng & Chen, Guanrong & Feng, Zhaosheng, 2008. "Synchronization in a class of weighted complex networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5616-5622.
    3. F. W. S. Lima, 2015. "Evolution of egoism on semi-directed and undirected Barabási-Albert networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 26(12), pages 1-9.
    4. L. da F. Costa & L. E.C. da Rocha, 2006. "A generalized approach to complex networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 237-242, March.
    5. Perc, Matjaž, 2010. "Zipf’s law and log-normal distributions in measures of scientific output across fields and institutions: 40 years of Slovenia’s research as an example," Journal of Informetrics, Elsevier, vol. 4(3), pages 358-364.
    6. Florian Blöchl & Fabian J. Theis & Fernando Vega-Redondo & Eric O'N. Fisher, 2010. "Which Sectors of a Modern Economy are most Central?," CESifo Working Paper Series 3175, CESifo.
    7. M. C. González & A. O. Sousa & H. J. Herrmann, 2004. "Opinion Formation On A Deterministic Pseudo-Fractal Network," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 45-57.
    8. A. Chatterjee, 2009. "Kinetic models for wealth exchange on directed networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 67(4), pages 593-598, February.
    9. D Dylan Johnson Restrepo & Neil F Johnson, 2017. "Unraveling the Collective Dynamics of Complex Adaptive Biomedical Systems," Current Trends in Biomedical Engineering & Biosciences, Juniper Publishers Inc., vol. 8(5), pages 118-132, September.
    10. A. Santiago & J. P. Cárdenas & M. L. Mouronte & V. Feliu & R. M. Benito, 2008. "Modeling The Topology Of Sdh Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(12), pages 1809-1820.
    11. Slobodan Maletić & Danijela Horak & Milan Rajković, 2012. "Cooperation, Conflict And Higher-Order Structures Of Social Networks," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 15(supp0), pages 1-29.
    12. Giorgio Fagiolo & Marco Valente & Nicolaas J. Vriend, 2009. "A Dynamic Model of Segregation in Small-World Networks," Lecture Notes in Economics and Mathematical Systems, in: Ahmad K. Naimzada & Silvana Stefani & Anna Torriero (ed.), Networks, Topology and Dynamics, pages 111-126, Springer.
    13. H. Lin & C.-X. Wu, 2006. "Dynamics of congestion transition triggered by multiple walkers on complex networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 51(4), pages 543-547, June.
    14. Derzsi, A. & Derzsy, N. & Káptalan, E. & Néda, Z., 2011. "Topology of the Erasmus student mobility network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2601-2610.
    15. Gómez-Gardeñes, J. & Moreno, Y. & Floría, L.M., 2005. "Michaelis–Menten dynamics in complex heterogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 265-281.
    16. G. De Masi & Y. Fujiwara & M. Gallegati & B. Greenwald & J. E. Stiglitz, 2009. "An Analysis of the Japanese Credit Network," Papers 0901.2384, arXiv.org, revised Nov 2010.
    17. P. Toranj Simin & Gholam Reza Jafari & Marcel Ausloos & Cesar Federico Caiafa & Facundo Caram & Adeyemi Sonubi & Alberto Arcagni & Silvana Stefani, 2018. "Dynamical phase diagrams of a love capacity constrained prey–predator model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(2), pages 1-18, February.
    18. Tibély, Gergely, 2012. "Criterions for locally dense subgraphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1831-1847.
    19. A. O. Sousa & T. Yu-Song & M. Ausloos, 2008. "Effects of agents' mobility on opinion spreading in Sznajd model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 66(1), pages 115-124, November.
    20. Selen Onel & Abe Zeid & Sagar Kamarthi, 2011. "The structure and analysis of nanotechnology co-author and citation networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(1), pages 119-138, October.

    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:460:y:2016:i:c:p:1-15. 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.