Geodesic
Mathematical modeling of autowave processes in a cell with nanostructured liquid
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Tome 165 (2019), pp. 80-87

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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. 
@article{INTO_2019_165_a7,
     author = {V. V. Chekanov and N. V. Kandaurova and V. S. Chekanov and M. Yu. Shevchenko and S. R. Mirzahanov},
     title = {Mathematical modeling of autowave processes in a cell with nanostructured liquid},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {80--87},
     publisher = {mathdoc},
     volume = {165},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_165_a7/}
}
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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. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Tome 165 (2019), pp. 80-87. http://geodesic.mathdoc.fr/item/INTO_2019_165_a7/