Abstract:
We suggest a method allowing to investigate existence and the measure of proximity between the stationary solutions to continuous and discontinuous neural fields with microstructure. The present part involves a theorem on solvability of such equations based on topological degree theory, and a theorem on continuous dependence of the solutions under the transition from continuous to discontinuous activation function using compactness in a special topology.
Keywords:
mathematical neuroscience, neural field models with microstructure, solvability, continuous dependence on parameters.
The work is partially supported by the Russian Fund for Basic Research (projects №№ 17-41-680975, 18-31-00227).
Received: 15.01.2018
Bibliographic databases:
Document Type:
Article
UDC:
51-76, 517.988
Language: Russian
Citation:
E. O. Burlakov, M. A. Nasonkina, “On connection between continuous and discontinuous neural field models with microstructure I. General theory”, Tambov University Reports. Series: Natural and Technical Sciences, 23:121 (2018), 17–30
\Bibitem{BurNas18}
\by E.~O.~Burlakov, M.~A.~Nasonkina
\paper On connection between continuous and discontinuous neural field models with microstructure I. General theory
\jour Tambov University Reports. Series: Natural and Technical Sciences
\yr 2018
\vol 23
\issue 121
\pages 17--30
\mathnet{http://mi.mathnet.ru/vtamu87}
\crossref{https://doi.org/10.20310/1810-0198-2018-23-121-17-30}
\elib{https://elibrary.ru/item.asp?id=32697170}
This publication is cited in the following 3 articles:
A. S. Lanina, E. A. Pluzhnikova, “O svoistvakh reshenii differentsialnykh sistem, modeliruyuschikh elektricheskuyu aktivnost golovnogo mozga”, Vestnik rossiiskikh universitetov. Matematika, 27:139 (2022), 270–283
R. Atmaniya, E. O. Burlakov, I. N. Malkov, “O resheniyakh tipa «koltso» uravnenii neironnogo polya”, Vestnik rossiiskikh universitetov. Matematika, 26:136 (2021), 363–371
E. O. Burlakov, I. N. Malkov, “O svyazi nepreryvnykh i razryvnykh modelei neironnykh polei s mikrostrukturoi: II. Radialno simmetrichnye statsionarnye resheniya v 2D («bampy»)”, Vestnik rossiiskikh universitetov. Matematika, 25:129 (2020), 6–17
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