ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

stochastic bifurcations

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

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.

Noise-induced effects in the double-well oscillator with variable friction

A model of bistable stochastic oscillator with dynamical variables depending on dissipation is offered. Considered system demonstrates stochastic P-bifurcations and non-monotonic dependence of the mean oscillation frequency on the noise intensity. An effective noise intensity and an effective potential are introduced for a quantitative description of the observed effects.