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Nelin. Dinam., 2012, Volume 8, Number 3, Pages 497–505 (Mi nd338)  

This article is cited in 3 scientific papers (total in 3 papers)

Two kinds of auto-oscillations in active medium with periodical border conditions

Andrey V. Slepnev, Tatyana E. Vadivasova

International Research Institute of Nonlinear Dynamics Saratov State University named after N. G. Chernyshevsky, Astrahanskaya st. 83, Saratov, 410026, Russia

Abstract: The model of an active medium with periodical boundary conditions is studied. The elementary cell is chosen to be FitzHugh–Nagumo oscillator. According to the values of parameters the elementary cell is able to be either in self-sustained regime or in excitable one. In both cases there are sustained oscillations in each elementary cell of the medium, but the causes of its initiation are different. In case of the former each cell in itself is auto-oscillator, in case of the latter the oscillations appear because of feedback which is provided by the periodical boundary conditions. In both cases the phenomenon of multistability is observed. The comparative analysis of the regimes mentioned above is carried out. There are shown that the dependencies of oscillations characteristics from the system parameters in either cases significantly differ from one another. The bifurcational type of the transition from one cell regime to another is ascertained for some modes. The influence of spatial-uncorrelated noise on the active medium behavior is considered. The average period of oscillations versus noise intensity relation is obtained.

Keywords: active medium, FitzHugh–Nagumo system, spatial structures, multistability, noise influence

Full text: PDF file (600 kB)
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UDC: 537.86, 530.182
MSC: 70Kxx, 39Axx
Received: 11.07.2012
Revised: 12.09.2012

Citation: Andrey V. Slepnev, Tatyana E. Vadivasova, “Two kinds of auto-oscillations in active medium with periodical border conditions”, Nelin. Dinam., 8:3 (2012), 497–505

Citation in format AMSBIB
\Bibitem{SleVad12}
\by Andrey~V.~Slepnev, Tatyana~E.~Vadivasova
\paper Two kinds of auto-oscillations in active medium with periodical border conditions
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 3
\pages 497--505
\mathnet{http://mi.mathnet.ru/nd338}


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    This publication is cited in the following articles:
    1. A. V. Slepnev, I. A. Shepelev, T. E. Vadivasova, “Noise-induced effects in an active medium with periodic boundary conditions”, Tech. Phys. Lett., 40:1 (2014), 62–64  crossref  adsnasa  isi  elib  elib  scopus
    2. A. V. Slepnev, I. A. Shepelev, T. E. Vadivasova, “Vynuzhdennaya sinkhronizatsiya beguschikh voln v aktivnoi srede v avtokolebatelnom i vozbudimom rezhimakh”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 22:2 (2014), 50–61  zmath  elib
    3. V. V. Chekanov, N. V. Kandaurova, V. S. Chekanov, M. Yu. Shevchenko, S. R. Mirzakhanov, “Matematicheskoe modelirovanie avtovolnovykh protsessov v yacheike s nanostrukturirovannoi zhidkostyu”, Materialy IV Mezhdunarodnoinauchnoi konferentsii “Aktualnye problemy prikladnoi matematiki”. Kabardino-Balkarskaya respublika, Nalchik, Prielbruse, 2226 maya 2018 g. ChastI, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 165, VINITI RAN, M., 2019, 80–87  mathnet  crossref
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