Abstract:
In the present research, existence and stability of ring solutions to two-dimensional Amari neural field equation with periodic microstructure and Heaviside activation function are studied. Results on dependence of the inner and the outer radii of the ring solutions are obtained. Necessary conditions for existence and sufficient conditions for non-existence of radial travelling waves are formulated for homogeneous neural medium and neural media with mild periodic microstructure. Theoretical results obtained are illustrated with a concrete example based on a connectivity function commonly used in the neuroscience community.
Keywords:
mathematical neuroscience, neural field models with microstructure, two-dimensional neural field equation, ring solution, existence of solutions, stability of solutions, radial travelling waves.
Citation:
R. Atmania, E. O. Burlakov, I. N. Malkov, “On existence and stability of ring solutions to Amari neural field equation with periodic microstructure and Heaviside activation function”, Russian Universities Reports. Mathematics, 27:140 (2022), 318–327
\Bibitem{AtmBurMal22}
\by R.~Atmania, E.~O.~Burlakov, I.~N.~Malkov
\paper On existence and stability of ring solutions to Amari neural field equation with periodic microstructure and Heaviside activation function
\jour Russian Universities Reports. Mathematics
\yr 2022
\vol 27
\issue 140
\pages 318--327
\mathnet{http://mi.mathnet.ru/vtamu268}
\crossref{https://doi.org/10.20310/2686-9667-2022-27-140-318-327}
Linking options:
https://www.mathnet.ru/eng/vtamu268
https://www.mathnet.ru/eng/vtamu/v27/i140/p318
This publication is cited in the following 2 articles:
Ivan Malkov, Evgenii Burlakov, Vitaly Verkhlyutov, Vadim Ushakov, Studies in Computational Intelligence, 1179, Advances in Neural Computation, Machine Learning, and Cognitive Research VIII, 2025, 244
Ivan Malkov, Evgenii Burlakov, Vitaly Verkhlyutov, Vadim Ushakov, Advances in Neural Computation, Machine Learning, and Cognitive Research VIII, 2024, 244
Citation in format AMSBIB
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