Andrei Slepnev

    Astrakhanskaya st., 83 410026, Saratov, Russia
    Saratov State University


    Slepnev A. V., Vadivasova T. E.
    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
    Citation: Slepnev A. V., Vadivasova T. E.,  Two kinds of auto-oscillations in active medium with periodical border conditions, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 3, pp.  497-505
    Slepnev A. V., Vadivasova T. E., Listov A. S.
    The model of a self-oscillatory medium whose cells represent Anishchenko-Astakhov self-sustained oscillators is studied. Under periodic boundary conditions the phenomenon of multistability is observed in the medium — the stable self-sustained oscillatory modes with different spatial structures coexist and can be realized by means of appropriately chosen initial conditions. The study of the time period doubling bifurcations is performed for different modes. It is shown that the evolution of the modes between two successive bifurcations leads to the complexification of instantaneous spatial profile and to the appearance of small-scale spatial oscillations. The distribution of the instantaneous phase shift along the medium is studied in different regimes. The influence of local noise source on the spatial structures is considered. It is demonstrated that noise can induce switchings between different regimes. The mechanism of such switchings is explored.
    Keywords: self-oscillatory medium, period doubling, spatial structures, multistability, noise excitation
    Citation: Slepnev A. V., Vadivasova T. E., Listov A. S.,  Multistability, period doubling and traveling waves suppression by noise excitation in a nonlinear self-oscillatory medium with periodic boundary conditions, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 4, pp.  755-767

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