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

stochastic bifurcation

The studies of the arising of oscillations in the quasi­harmonic model of the self­sustained oscillatory medium under multiplicative noise excitation

The multiplicative noise influence on the self-sustained oscillatory medium near the oscillation threshold is studied. The chain of the identical quasi-harmonic self-sustained oscillators with the periodic boundary conditions is taken as a simplest model of the oscillatory medium. The parameters of the oscillators are modulated with the white Gaussian noise. The stochastic bifurcations are analyzed for the cases of homogenous and spatially-nonhomogenous noise. 

Period doubling bifurcations and noise excitation effects in a multistable self-sustained oscillatory medium

The model of a self-oscillatory medium composed from the elements with complex self-oscillatory behavior is studied. Under periodic boundary conditions the stable selfoscillatory 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.

Noise induced parametric instability and stochastic oscillations in the oscillator with nonlinear dissipation

The appearance of the instability of oscillator equilibrium state in a case of noisy modulation of the natural frequency is considered in the work. The threshold of instability and the properties of stochastic oscillations arising over the threshold are studied for the different noise characteristics.

Stochastic bifurcations

The modern knowledges of bifurcations of dynamical systems in the presence of noise are presenred. The main definitions are given and certain typical examples of the bifurcations in the presence of additive and multiplicative noise are considered.

Noise-induced bifurcations in bistable oscillator

We investigate bistable oscillator under the influence of additive, white and colored, noise. We have found noise-induced bifurcations that consist in a qualitative change of stationary distribution of oscillations amplitude. In the region of bimodal distribution the effect of coherent resonance takes place both for white and colored noise.

Experimental study of stochastic phenomena in a self­sustained oscillator with subcritical andronov–hopf 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.