ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Slepnev A. V., Vadivasova T. E. Period doubling bifurcations and noise excitation effects in a multistable self-sustained oscillatory medium. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 4, pp. 53-67. DOI: 10.18500/0869-6632-2011-19-4-53-67

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
537.86, 530.182
DOI: 
10.18500/0869-6632-2011-19-4-53-67

Period doubling bifurcations and noise excitation effects in a multistable self-sustained oscillatory medium

Autors: 
Slepnev Andrej Vjacheslavovich, Saratov State University
Vadivasova Tatjana Evgenevna, Saratov State University
Abstract: 

The model of a self-oscillatory medium composed from the elements with complex self-oscillatory behavior is studied. Under periodic boundary conditions the stable selfoscillatory regimes in the form of traveling waves with different phase shifts are coexisted in medium. The study of mechanisms of the oscillations period doubling in time is performed for different coexisted modes. For all observed spatially-non-uniform regimes (traveling waves) the period doubling occurs through the appearance of time-quasiperiodic oscillations and their further evolution. The period doubling result in multistability development. For each mode with the given phase shift the different stable non-uniform structures, which are differed by the distribution of oscillations characteristics in space, emerge. The influence of a noise signal leads to the shift of doubling bifurcation in the direction of the control parameter increasing. When the value of control parameter is fixed the stochastic bifurcations of contingency, which are shown in reduction of extremes numbers in the probabilistic distribution, are observed with the increasing of noise intensity. When the noise is sufficiently great the spatially-non-uniform modes corresponding to nonzero phase shifts disappear.

Key words: 
Self-oscillatory medium
multistability
period doubling
spatial structures
stochastic bifurcation
P-bifurcation
noise
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Received: 
08.11.2010
Accepted: 
08.07.2011
Published: 
30.09.2011
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