Dynamics of Periodic Waves in a Neural Field Model

Nikolai Bessonov, Anne Beuter, Sergei Trofimchuk and Vitaly Volpert
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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
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

Mathematics, 2020, vol. 8, issue 7, 1-17

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.

Keywords: neural field model; integro-differential equation; waves; brain stimulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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