Stochastic dynamics and chaos in the 3D Hindmarsh-Rose model

Lev Ryashko, Irina Bashkirtseva, Evdokia Slepukhina, Sergei Fedotov

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    Abstract

    We study the effect of random disturbances on the three-dimensional Hindmarsh-Rose model of neural activity. In a parametric zone, where the only attractor of the system is a stable equilibrium, a stochastic generation of bursting oscillations is observed. For a sufficiently small noise, random states concentrate near the equilibrium. With an increase of the noise intensity, along with small-amplitude oscillations around the equilibrium, bursts are observed. The relationship of the noise-induced generation of bursts with system transitions from order to chaos is discussed. For a quantitative analysis of these stochastic phenomena, an approach based on the stochastic sensitivity function technique is suggested.

    Original languageEnglish
    Title of host publicationInternational Conference of Computational Methods in Sciences and Engineering 2016, ICCMSE 2016
    EditorsZacharoula Kalogiratou, Theodore E. Simos, Theodore Monovasilis, Theodore E. Simos, Theodore E. Simos
    PublisherAmerican Institute of Physics
    ISBN (Electronic)9780735414549
    DOIs
    Publication statusPublished - 6 Dec 2016
    EventInternational Conference of Computational Methods in Sciences and Engineering 2016 - Athens, Greece
    Duration: 17 Mar 201620 Mar 2016

    Publication series

    NameAIP Conference Proceedings
    Volume1790
    ISSN (Print)0094-243X
    ISSN (Electronic)1551-7616

    Conference

    ConferenceInternational Conference of Computational Methods in Sciences and Engineering 2016
    Abbreviated titleICCMSE 2016
    Country/TerritoryGreece
    CityAthens
    Period17/03/1620/03/16

    Keywords

    • excitability
    • Hindmarsh-Rose model
    • noise-induced chaotization
    • noise-induced oscillations
    • stochastic sensitivity

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