Preprint Article Version 1 This version is not peer-reviewed

Dynamics of Periodic Waves in a Neural Field Model

Version 1 : Received: 7 March 2020 / Approved: 8 March 2020 / Online: 8 March 2020 (06:55:15 CET)

A peer-reviewed article of this Preprint also exists.

Bessonov, N.; Beuter, A.; Trofimchuk, S.; Volpert, V. Dynamics of Periodic Waves in a Neural Field Model. Mathematics 2020, 8, 1076. Bessonov, N.; Beuter, A.; Trofimchuk, S.; Volpert, V. Dynamics of Periodic Waves in a Neural Field Model. Mathematics 2020, 8, 1076.

Journal reference: Mathematics 2020, 8, 1076
DOI: 10.3390/math8071076

Abstract

Periodic travelling 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 influence of asymmetric connectivity functions and of time delay on the emergence of periodic waves and on their properties. Nonlinear wave dynamics is 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.

Subject Areas

neural field models; integrodifferential equations; wave; brain stimulation

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