EXPERIMENTAL STUDY OF STOCHASTIC PHENOMENA IN A SELFSUSTAINED OSCILLATOR WITH SUBCRITICAL ANDRONOV–HOPF BIFURCATION
Cite this article as:
Semenov V. V., Listov А. S., Vadivasova Т. Е. 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: https://doi.org/10.18500/0869-6632-2014-22-5-43-57
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.
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BibTeX
author = {Vladimir Victorovich Semenov and А. S. Listov and Т. Е. Vadivasova },
title = {EXPERIMENTAL STUDY OF STOCHASTIC PHENOMENA IN A SELFSUSTAINED OSCILLATOR WITH SUBCRITICAL ANDRONOV–HOPF BIFURCATION},
year = {2014},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {22},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/experimental-study-of-stochastic-phenomena-in-selfsustained-oscillator-with-subcritical},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2014-22-5-43-57},pages = {43--57},issn = {0869-6632},
keywords = {Subcritical Andronov–Hopf bifurcation,additive noise,parametric noise,stochastic bifurcation,bifurcational interval.},
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. }}