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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.
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.
Keywords
neural field models; integrodifferential equations; wave; brain stimulation
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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