Geodesic
Two kinds of auto-oscillations in active medium with periodical border conditions
Russian journal of nonlinear dynamics, Tome 8 (2012) no. 3, pp. 497-505

Voir la notice de l'article provenant de la source Math-Net.Ru

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, multistability
Mots-clés : spatial structures, noise influence. 
@article{ND_2012_8_3_a4,
     author = {Andrey V. Slepnev and Tatyana E. Vadivasova},
     title = {Two kinds of auto-oscillations in active medium with periodical border conditions},
     journal = {Russian journal of nonlinear dynamics},
     pages = {497--505},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2012_8_3_a4/}
}
TY  - JOUR
AU  - Andrey V. Slepnev
AU  - Tatyana E. Vadivasova
TI  - Two kinds of auto-oscillations in active medium with periodical border conditions
JO  - Russian journal of nonlinear dynamics
PY  - 2012
SP  - 497
EP  - 505
VL  - 8
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2012_8_3_a4/
LA  - ru
ID  - ND_2012_8_3_a4
ER  - 
%0 Journal Article
%A Andrey V. Slepnev
%A Tatyana E. Vadivasova
%T Two kinds of auto-oscillations in active medium with periodical border conditions
%J Russian journal of nonlinear dynamics
%D 2012
%P 497-505
%V 8
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2012_8_3_a4/
%G ru
%F ND_2012_8_3_a4
Andrey V. Slepnev; Tatyana E. Vadivasova. Two kinds of auto-oscillations in active medium with periodical border conditions. Russian journal of nonlinear dynamics, Tome 8 (2012) no. 3, pp. 497-505. http://geodesic.mathdoc.fr/item/ND_2012_8_3_a4/