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Vestnik Samarskogo Universiteta. Estestvenno-Nauchnaya Seriya, 2018, Volume 24, Issue 4, Pages 33–40
DOI: https://doi.org/10.18287/2541-7525-2018-24-4-33-40 (Mi vsgu597) 		 
Mathematics

Parametrization of invariant manifolds of slow motions

V. A. Sobolev, E. A. Shchepakina, E. A. Tropkina

Samara National Research University, 34, Moskovskoye shosse, Samara, 443086, Russian Federation
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DOI: https://doi.org/10.18287/2541-7525-2018-24-4-33-40
Abstract: The method of integral manifolds is used to study the multidimensional systems of differential equations. This approach allows to solve an important problem of order reduction of differential systems. If a slow invariant manifold cannot be described explicitly then its parametrization is used for the system order reduction. In this case, either a part of the fast variables, or all fast variables, supplemented by a certain number of slow variables, can play a role of the parameters.
Keywords: singular perturbations, integral manifold, order reduction, asymptotic expansion, parametrization, differential equations, fast variables, slow variables.
Funding agency Grant number
Russian Foundation for Basic Research 16-41-630524_р_а
16-41-630529_р_а
Ministry of Education and Science of the Russian Federation
The study was carried out with the financial support of the Russian Foundation for Basic Research and the Government of the Samara Region within the framework of research projects No. 16-41-630524 р−а and No. 16-41-630529 р−а and the Ministry of Education and Science of the Russian Federation within the framework of the Samara University competitiveness improvement program (2013–2020).
Received: 26.09.2018
Bibliographic databases:
Document Type: Article
UDC: 517.928
Language: Russian
Citation: V. A. Sobolev, E. A. Shchepakina, E. A. Tropkina, “Parametrization of invariant manifolds of slow motions”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 24:4 (2018), 33–40
Citation in format AMSBIB
\Bibitem{SobShcTro18}
\by V.~A.~Sobolev, E.~A.~Shchepakina, E.~A.~Tropkina
\paper Parametrization of invariant manifolds of slow motions
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2018
\vol 24
\issue 4
\pages 33--40
\mathnet{http://mi.mathnet.ru/vsgu597}
\crossref{https://doi.org/10.18287/2541-7525-2018-24-4-33-40}
\elib{https://elibrary.ru/item.asp?id=37118580}
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