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


влияние шума

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 self­sustained oscillatory medium near the oscillation threshold is studied. The chain of the identical quasi­harmonic self­sustained 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 spatially­nonhomogenous noise.

Influence of fluctuations on evolution of three-dimensional torus in nonautonomous system

The transition to chaos through the destruction of three-dimensional torus is studied in a nonautonomous system with quasi-periodic impact as example. Analysis is carried out of the in?uence both of additive noise and frequency ?uctuations impact on the stability of three-dimensional torus. It is shown that under the in?uence of additive noise and frequency ?uctuations impact Lyapunov exponent remains negative. This allows to conclude that in this model three-dimensional torus is structurally stable in contrast to theautonomous system.