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Article Dans Une Revue Mathematics Année : 2020

Dynamics of Periodic Waves in a Neural Field Model

Résumé

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.

Dates et versions

hal-03027337 , version 1 (27-11-2020)

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Nikolai Bessonov, Anne Beuter, Sergei Trofimchuk, Vitaly Volpert. Dynamics of Periodic Waves in a Neural Field Model. Mathematics , 2020, 8 (7), pp.1-17. ⟨10.3390/math8071076⟩. ⟨hal-03027337⟩
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