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

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Semenov V. V., Listov A. S., Vadivasova T. E. Experimental study of stochastic phenomena in a self­sustained oscillator with subcritical andronov–hopf bifurcation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, vol. 22, iss. 5, pp. 43-57. DOI: 10.18500/0869-6632-2014-22-5-43-57

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
537.86; 519.21
DOI: 
10.18500/0869-6632-2014-22-5-43-57

Experimental study of stochastic phenomena in a self­sustained oscillator with subcritical andronov–hopf bifurcation

Autors: 
Semenov V. V., Saratov State University
Listov Aleksandr Serafimovich, Saratov State University
Vadivasova Tatjana Evgenevna, Saratov State University
Abstract: 

The effect of noise on the self­sustained oscillator near subcritical Andronov–Hopf bifurcation is studied in numerical and full­scale experiments. Van der Pol oscillator is chosen as base model for investigation. The influence of both additive and multiplicative Gaussian white noise is considered. The regularities of evolution of the probability distribution in the self­sustained oscillator are analyzed with increase of the noise intensity for the cases of additive and parametric noise. The existence of a bifurcation interval is established experimentally for subcritical Andronov–Hopf bifurcation in the presence of additive noise. Besides of this, the  existence of a bifurcation interval is shown for the tangent bifurcation. The postponed character of the Andronov–Hopf bifurcation is confirmed for a multiplicative (parametric) noise excitation. The results of the full­scale modeling are compared with the numerical data.

Key words: 
Subcritical Andronov–Hopf bifurcation
additive noise
parametric noise
stochastic bifurcation
bifurcational interval
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Received: 
02.09.2014
Accepted: 
19.11.2014
Published: 
31.03.2015
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