Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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
Full-text PDF (231 kB)
References:
PDF
HTML
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}
Linking options:
  • https://www.mathnet.ru/eng/into463
  • https://www.mathnet.ru/eng/into/v165/p10
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
    Statistics & downloads:
    Abstract page:223
    Full-text PDF :86
    References:22
    First page:1
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024