IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v414y2014icp181-193.html
   My bibliography  Save this article

Abstract phase space networks describing reactive dynamics

Author

Listed:
  • Provata, A.
  • Panagakou, E.

Abstract

An abstract network approach is proposed for the description of the dynamics in reactive processes. The phase space of the variables (concentrations in reactive systems) is partitioned into a finite number of segments, which constitute the nodes of the abstract network. Transitions between the nodes are dictated by the dynamics of the reactive process and provide the links between the nodes. These are weighted networks, since each link weight reflects the transition rate between the corresponding states–nodes. With this construction the network properties mirror the dynamics of the underlying process and one can investigate the system properties by studying the corresponding abstract network. As a working example the Lattice Limit Cycle (LLC) model is used. Its corresponding abstract network is constructed and the transition matrix elements are computed via Kinetic (Dynamic) Monte Carlo simulations. For this model it is shown that the degree distribution follows a power law with exponent −1, while the average clustering coefficient c(N) scales with the network size (number of nodes) N as c(N)∼N−ν,ν≃1.46. The computed exponents classify the LLC abstract reactive network into the scale-free networks. This conclusion corroborates earlier investigations demonstrating the formation of fractal spatial patterns in LLC reactive dynamics due to stochasticity and to clustering of homologous species. The present construction of abstract networks (based on the partition of the phase space) is generic and can be implemented with appropriate adjustments in many dynamical systems and in time series analysis.

Suggested Citation

  • Provata, A. & Panagakou, E., 2014. "Abstract phase space networks describing reactive dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 181-193.
    • Handle: RePEc:eee:phsmap:v:414:y:2014:i:c:p:181-193
    DOI: 10.1016/j.physa.2014.06.063
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114005445
    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.2014.06.063?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. Dong, Yan & Huang, Wenwen & Liu, Zonghua & Guan, Shuguang, 2013. "Network analysis of time series under the constraint of fixed nearest neighbors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 967-973.
    2. G. A. Tsekouras & A. Provata, 2006. "Fractal formations in the Lattice Limit Cycle model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 52(1), pages 107-111, July.
    Full references (including those not matched with items on IDEAS)

    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. Wang, Minggang & Tian, Lixin & Xu, Hua & Li, Weiyu & Du, Ruijin & Dong, Gaogao & Wang, Jie & Gu, Jiani, 2017. "Systemic risk and spatiotemporal dynamics of the consumer market of China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 188-204.
    2. Tang, Jinjun & Wang, Yinhai & Wang, Hua & Zhang, Shen & Liu, Fang, 2014. "Dynamic analysis of traffic time series at different temporal scales: A complex networks approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 303-315.
    3. Wang, Minggang & Tian, Lixin, 2016. "From time series to complex networks: The phase space coarse graining," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 456-468.

    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:414:y:2014:i:c:p:181-193. 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.