Email this article On existence and stability of ring solutions to Amari neural field equation with periodic microstructure and Heaviside activation function
- Authors: Atmania R.1, Burlakov E.O.1,2, Malkov I.N.1
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Affiliations:
- Tyumen State University
- Derzhavin Tambov State University
- Issue: Vol 27, No 140 (2022)
- Pages: 318-327
- Section: Original articles
- URL: https://bakhtiniada.ru/2686-9667/article/view/296487
- ID: 296487
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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.
About the authors
Rachid Atmania
Tyumen State University
Email: atmania.rachid@gmail.com
ORCID iD: 0000-0002-2194-1497
Post-Graduate Student
Russian Federation, 6 Volodarskogo St., Tyumen 625003, Russian FederationEvgenii O. Burlakov
Tyumen State University; Derzhavin Tambov State University
Author for correspondence.
Email: eb_@bk.ru
ORCID iD: 0000-0002-7286-9456
PhD, Senior Researcher at X-Bio Institute; Researcher at the Research and Educational Center “Fundamental Mathematical Research”
Russian Federation, 6 Volodarskogo St., Tyumen 625003, Russian Federation; 33 Internatsionalnaya St., Tambov 392000, Russian FederationIvan N. Malkov
Tyumen State University
Email: i.n.malkov@yandex.ru
ORCID iD: 0000-0001-5845-5591
Post-Graduate Student, Institute of Mathematics and Computer Science
Russian Federation, 6 Volodarskogo St., Tyumen 625003, Russian FederationReferences
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