IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v162y2022ics0960077922006282.html
   My bibliography  Save this article

Impact of local timescales in a cellular automata model of excitable media

Author

Listed:
  • Moitra, Promit
  • Sen, Abhijit

Abstract

A cellular automata system known as the Greenberg-Hastings cellular automata (GHCA), with cyclic and excitable individual dynamics, provides a useful paradigm for modeling emergent phenomena in an excitable medium. Most past studies of GHCA have investigated the asymptotic dynamics of the system, assuming fixed extents for the active and passive dynamical phases. This study is a systematic investigation of the relationship between the dynamical properties of individual cells of a small system implementing excitable dynamics, and the emergent system wide asymptotic state. The impact of the temporal extents of individual dynamical phases (τa, τp), on the probability of persistence P(τa,τp), defined as the fraction of initial configurations which sustain spatiotemporal oscillations asymptotically, is examined for each unique configuration of the system. The main result obtained is that the probability of persistence P(τa, τp) assumes a characteristic sigmoidal form, as the dynamical behaviour of the system transitions from absolute quiescence to persistent spatiotemporal oscillations, with respect to the parameters (τa, τp). A plot of the numerical findings in the (τa, τp) space provides a consolidated view of their impact on the emergent behaviour of the system. In conclusion, some implications of the methods and results presented in this work, to the study of emergent phenomena in excitable systems, are discussed.

Suggested Citation

  • Moitra, Promit & Sen, Abhijit, 2022. "Impact of local timescales in a cellular automata model of excitable media," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006282
    DOI: 10.1016/j.chaos.2022.112418
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922006282
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112418?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. Kohar, Vivek & Sinha, Sudeshna, 2013. "Emergence of epidemics in rapidly varying networks," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 127-134.
    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. Nag, Mayurakshi & Poria, Swarup, 2016. "Synchronization in a network of delay coupled maps with stochastically switching topologies," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 9-16.
    2. Claudio J. Tessone, "undated". "Collective behaviour induced by network volatility," Working Papers ETH-RC-14-010, ETH Zurich, Chair of Systems Design.
    3. Chaurasia, Sudhanshu Shekhar & Choudhary, Anshul & Shrimali, Manish Dev & Sinha, Sudeshna, 2019. "Suppression and revival of oscillations through time-varying interaction," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 249-254.

    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:chsofr:v:162:y:2022:i:c:s0960077922006282. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.