stochastic bifurcation

The effect of noise on the self­sustained oscillator near subcritical Andronov–Hopf bifurcation is studied in numerical and full­scale experiments. Van der Pol oscillator is chosen as base model for investigation. The influence of both additive and multiplicative Gaussian white noise is considered. The regularities of evolution of the probability distribution in the self­sustained oscillator are analyzed with increase of the noise intensity for the cases of additive and parametric noise.

The model of a self-oscillatory medium composed from the elements with complex self-oscillatory behavior is studied. Under periodic boundary conditions the stable self-oscillatory regimes in the form of traveling waves with different phase shifts are coexisted in medium. The study of mechanisms of the oscillations period doubling in time is performed for different coexisted modes. For all observed spatially-non-uniform regimes (traveling waves) the period doubling occurs through the appearance of time-quasiperiodic oscillations and their further evolution.