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Vadivasova T. E., Malyaev V. S. Bifurcations in van der pol oscillator with a hard excitation in a presence of parametrical noise: quasi-harmonic analyzes and the numerical simulations. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 2, pp. 113-134. DOI: 10.18500/0869-6632-2013-21-2-113-134

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Bifurcations in van der pol oscillator with a hard excitation in a presence of parametrical noise: quasi-harmonic analyzes and the numerical simulations

Vadivasova Tatjana Evgenevna, Saratov State University
Malyaev Vladimir Sergeevich, Saratov State University

In the work the behavior of a van der Pol oscillator with a hard excitation is considered near the excitation threshold under parametrical (multiplicative) Gaussian white noise disturbances, and in a case of the two noise sources presence: parametrical one and additive noise. The evolution of probability distribution is studied when a control parameter and a noise intensity are changed. A comparison of the theoretical results, obtained in the quasi-harmonic approach with the results  of numerical solutions of the oscillator stochastic equations is fulfilled.

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