Geodesic
Experimental investigation of stochastic Andronov--Hopf bifurcation in self-sustained oscillators with additive and parametric noise
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 3, pp. 421-434

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Effects of noisy influence on oscillators near oscillation threshold are studied by means of numerical simulation and natural experiments. Two qualitative different models (Van der Pol and Anishchenko–Astakhov self-sustained oscillators) are considered. Evolution laws of probabilistic distribution with increase of noise intensity are established for two cases: addition of additive and parametric white gaussian noise in researched systems. It is shown that the noise destroys the distribution form, which is typical for self-oscillations, that leads to shift of bifurcation to direction of excitation parameter increase. The existence of bifurcation interval, which corresponds with gradual transition to regime of self-oscillation, was detected from experiments with additive noise.
Keywords: noisy dynamical systems, self-oscillations, additive noise, parametric noise.
Mots-clés : bifurcations 
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     author = {Vladimir V. Semenov and Kirill V. Zakoretskii and Tatyana E. Vadivasova},
     title = {Experimental investigation of stochastic {Andronov--Hopf} bifurcation in self-sustained oscillators with additive and parametric noise},
     journal = {Russian journal of nonlinear dynamics},
     pages = {421--434},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2013_9_3_a2/}
}
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Vladimir V. Semenov; Kirill V. Zakoretskii; Tatyana E. Vadivasova. Experimental investigation of stochastic Andronov--Hopf bifurcation in self-sustained oscillators with additive and parametric noise. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 3, pp. 421-434. http://geodesic.mathdoc.fr/item/ND_2013_9_3_a2/