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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 165, Pages 80–87
DOI: https://doi.org/10.36535/0233-6723-2019-165-80-87 (Mi into469) 		 
Mathematical modeling of autowave processes in a cell with nanostructured liquid

V. V. Chekanova, N. V. Kandaurovab, V. S. Chekanovb, M. Yu. Shevchenkoc, S. R. Mirzahanova

a North-Caucasus Federal University
b MIREA — Russian Technological University, Moscow
c Optosystems Ltd., Troitsk, Moscow
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DOI: https://doi.org/10.36535/0233-6723-2019-165-80-87
Abstract: In this paper, a solution of the mathematical model of an autowave process in a thin near-electrode layer of a magnetic fluid is found. A modification of the FitzHugh–Nagumo system taken as the basis of the mathematical model made it possible to obtain results similar to a full-scale experiment. As a criterion for the adequacy of the model, we use a visual correspondence to the experiment and the presence in the solution of typical phenomena observed in the autowave process, such as reverbs, pacemakers, encircling of obstacles, etc.
Keywords: autowave, self-organization, magnetic fluid, FitzHugh–Nagumo model, mathematical modeling.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 3.5385.2017/8.9
This work was performed as a part of the state assignment No. 3.5385.2017/8.9 “Experimental study and mathematical modeling of interphase and surface phenomena in thin films of nanostructured magnetic fluids”.
Bibliographic databases:
Document Type: Article
UDC: 517.958; 538.97
MSC: 90-08
Language: Russian
Citation: V. V. Chekanov, N. V. Kandaurova, V. S. Chekanov, M. Yu. Shevchenko, S. R. Mirzahanov, “Mathematical modeling of autowave processes in a cell with nanostructured liquid”, 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, 80–87
Citation in format AMSBIB
\Bibitem{CheKanChe19}
\by V.~V.~Chekanov, N.~V.~Kandaurova, V.~S.~Chekanov, M.~Yu.~Shevchenko, S.~R.~Mirzahanov
\paper Mathematical modeling of autowave processes in a cell with nanostructured liquid
\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 80--87
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into469}
\crossref{https://doi.org/10.36535/0233-6723-2019-165-80-87}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4030613}
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