Experimental investigation of stochastic Andronov--Hopf bifurcation in self-sustained oscillators with additive and parametric noise

Vladimir V. Semenov ; Kirill V. Zakoretskii ; Tatyana E. Vadivasova

Russian journal of nonlinear dynamics, Tome 9 (2013) no. 3, pp. 421-434.

Résumé

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.

Détail

Keywords: noisy dynamical systems, self-oscillations, additive noise, parametric noise.
Mots-clés : bifurcations

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