Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 165, Pages 10–20
DOI: https://doi.org/10.36535/0233-6723-2019-165-10-20 (Mi into463) 		 
On continuous and discontinuous models of neural fields

E. O. Burlakova, T. V. Zhukovskayab, E. S. Zhukovskiyc, N. P. Puchkovb

a Tyumen State University
b Tambov State Technical University
c Tambov State University named after G.R. Derzhavin
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DOI: https://doi.org/10.36535/0233-6723-2019-165-10-20
Abstract: This paper is devoted to research in mathematical neurobiology whose purpose is the establishment of a connection between approaches to the modeling of neural fields based on continuous and discontinuous equations. We review works on this topic and propose a new method for solving such problems based on Volterra's abstract inclusions, which allows one to generalize some previously obtained results.
Keywords: mathematical model, neural field, integral equation, Hammerstein equation, solvability, continuous dependence on parameters.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-00227_мол_а
17-01-00553_а
17-41-680975_р_а
17-51-12064_ННИО_а
Foundation for the Development of Theoretical Physics and Mathematics BASIS 18-1-7-37-1
Ministry of Science and Higher Education of the Russian Federation 3.8515.2017/БЧ
The work of E. O. Burlakov was supported by the Russian Foundation for Basic Research (project Nos. 17-41-680975 and 18-31-00227) and the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (project No. 18-1-7-37-1). The work of E. S. Zhukovskiy was supported by the Russian Foundation for Basic Research (project Nos. 17-01-00553, 17-41-680975, and 17-51-12064) and the Ministry of Education and Science of the Russian Federation (project No. 3.8515.2017/БЧ).
Bibliographic databases:
Document Type: Article
UDC: 517.988, 517.968
MSC: 47J05, 47H04, 35R09, 45K05, 47H30, 92F99
Language: Russian
Citation: E. O. Burlakov, T. V. Zhukovskaya, E. S. Zhukovskiy, N. P. Puchkov, “On continuous and discontinuous models of neural fields”, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 165, VINITI, Moscow, 2019, 10–20
Citation in format AMSBIB
\Bibitem{BurZhuZhu19}
\by E.~O.~Burlakov, T.~V.~Zhukovskaya, E.~S.~Zhukovskiy, N.~P.~Puchkov
\paper On continuous and discontinuous models of neural fields
\inbook Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics".
Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 165
\pages 10--20
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into463}
\crossref{https://doi.org/10.36535/0233-6723-2019-165-10-20}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4030607}
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