subcritical Andronov–Hopf bifurcation.

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.