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Dynamics of Periodic Waves in a Neural Field Model

Author

Listed:
  • Nikolai Bessonov

    (Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, 199178 Saint Petersburg, Russia)

  • Anne Beuter

    (Bordeaux INP, Avenue des Facultes, 33400 Talence, France
    CorStim SAS, 700 Avenue du Pic Saint Loup, 34090 Montpellier, France)

  • Sergei Trofimchuk

    (Instituto de Matematica y Fisica, Universidad de Talca, Casilla 747, Talca, Chile)

  • Vitaly Volpert

    (Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
    INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
    Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia)

Abstract

Periodic traveling waves are observed in various brain activities, including visual, motor, language, sleep, and so on. There are several neural field models describing periodic waves assuming nonlocal interaction, and possibly, inhibition, time delay or some other properties. In this work we study the influences of asymmetric connectivity functions and of time delay for symmetric connectivity functions on the emergence of periodic waves and their properties. Nonlinear wave dynamics are studied, including modulated and aperiodic waves. Multiplicity of waves for the same values of parameters is observed. External stimulation in order to restore wave propagation in a damaged tissue is discussed.

Suggested Citation

  • Nikolai Bessonov & Anne Beuter & Sergei Trofimchuk & Vitaly Volpert, 2020. "Dynamics of Periodic Waves in a Neural Field Model," Mathematics, MDPI, vol. 8(7), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1076-:d:379495
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    References listed on IDEAS

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    1. Vicente Botella-Soler & Mario Valderrama & Benoît Crépon & Vincent Navarro & Michel Le Van Quyen, 2012. "Large-Scale Cortical Dynamics of Sleep Slow Waves," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-10, February.
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