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


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.

Effect of noise on generalized synchronization of spatially extended systems described by Ginzburg–Landau equations

Effect of noise on generalized synchronization in spatially extended systems described by Ginzburg–Landau equations being in the spatio-temporal chaotic regime is studied. It is shown, that noise does not affect the synchronous regime threshold in such systems. The reasons of the revealed particularity have been explained by means of the modified system approach and confirmed by the results of numerical simulation. 

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.

Intermittency of type­-I with noise and eyelet intermittency

In this article we compare the characteristics of two types of the intermittent behavior (type-I intermittency in the presence of noise and eyelet intermittency) supposed hitherto to be the different phenomena. We prove that these effects are the same type of dynamics observed under different conditions. The correctness of our conclusion is proven by the consideration of different sample systems, such as quadratic map, van der Pol oscillator and Rossler system.

Experimental study of type I intermittency in a generator synchronized with external harmonic signal in the presence of noise

Аn experimental study of statistical properties of type I intermittency in the presence of noise is presented. For the first time an electronic experiment to study periodic oscillations synchronization destruction in case of small detuning in the presence of noise is held. The results are found to be in accordance with theory. 

Distribution of the laminar phases in the case of type-I intermittency with noise

This work is devoted to the intermittent behavior caused by the interplay between the dynamical mechanisms resulting in the type­I intermittency and the stochastic processes. The analytical consideration of the laminar phase distribution is given.

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.

Noises in resistive wall amplifier, caused by fluctuations in the electron beam

In this paper, noise in resistive wall amplifier – vacuum microwave device is studied, in which in which the gain is due to the phase shift between the electron beam and the alternating field components due to the presence of absorbing walls. It should be noted that in resistive wall amplifier, there is no need for a slowing system and that almost completely there is completely lacks the feedback between the output and the input. Recently, attention has been paid to it, in particular, because of the possibility of using metamaterials that increase the gain factor.

Noise in resistive-wall amplifier of m-type with «thick» beam

The aim of our research is to study the noise in the resistive-wall amplifier with crossed electric and magnetic fields with a beam of finite thickness. The theory of the O-type resistivewall amplifier is well known, at least as a classical example of using of waves with negative energy. Theory of resistive-wall amplifier M-type, in which negative energy waves are also used, has not been studied until recently. It seems interesting to study noise in a device with crossed fields, especially since early work mentioned a possible low noise level. Method.


The paper is devoted to the study of noise-induced intermittent behavior in multistable systems. Such task is an important enough because despite of a great interest of investigators to the study of multistability and intermittency, the problem connected with the detailed understanding of the processes taking place in the multistable dynamical systems in the presence of noise and theoretical description of arising at that intermittent behavior is still remain unsolved.