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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