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


Ring intermittency near the boundary of time scale synchronization

In this paper the intermittent behavior taking place near the boundary of the synchronous time scales of interacted chaotic oscillators being in the synchronous regime is studied. At the regime of time-scale synchronization the system demonstrates synchronous dynamics in a certain range of the time scales whereas the processes on the other time scales remain asynchronous. On the basis of analysis of statistical characteristics of the intermittent behavior, i.e.

Qualitative and numerical analysis of possible synchronous regimes for two inertially coupled van der pol oscillators

We consider a mechanical system consisting of two controlled masses that are attached to a movable platform via springs. We assume that at the absence of interaction the oscillations of both masses are described by the van der Pol equations. In this case, di?erent modes of synchronous behavior of the masses are observed: in-phase (complete), anti-phase and phase locking. By the methods of qualitative and numerical analysis, the boundaries of the stability domains of these regimes are obtained.

Nonlinear dynamics of helical electron flow in the regime of the virtual cathode forming

We produce the results of computer analysis of complex dynamics of non-relativistic electron beam being placed in crossed electric and magnetic ?elds, in the regime of a virtual cathod forming in additional braking ?eld. The modeling has been made in the framework of 2D numerical model in the geometry of magnetron-injector gun.

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 self-oscillatory regimes in the form of traveling waves with di?erent phase shifts are coexisted in medium. The study of mechanisms of the oscillations period doubling in time is performed for di?erent 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.

Dynamic regimes and multistability in the system of non- symmetrically coupled two-dimensional maps with period- doubling and neimark–sacker bifurcations

The phenomenon of multistability in the system of coupled universal two-dimensional maps which shows period-doubling and Neimark–Sacker bifurcations is investigated. The decreasing of possible coexisting attractors number, the evolution of the attractor basins, the disappearance of hyperchaos and three-dimensional torus while putting coupling asymmetryare exposed.

Multiparametrical analysis based on melnikov criterion and optimal chaos suppression in periodically driven dynamic systems

The results that illustrate the fruitfulness of the idea of optimal parametric correction for the analysis and optimization of the class of periodically driven chaotic systems are presented. Two problems that reveal the peculiarities of suppression of chaotic dynamics and present the method of regulation of the behavior of dissipative nonlinear oscillator were solved with the help of Melnikov criterion.

Wavelet analysis of sleep spindles on eeg and development of method for their automatic diagnostic

The detailed wavelet analysis of sleep electric brain activity, obtained from rats with genetic predisposition to absence-epilepsy, has been performed. Characteristic features of time-and-frequency structure of sleep spindles (oscillatory pattern, that serve as electroencephalographic correlate for slow-wave sleep) have been discovered in long-term electroencephalographic data. Operation has been performed using continuous wavelet transform.

Dynamics of local potentials of brain at the absence-epilepsy: empirical modelling

The EEG research technique on the basis of autoregressive models construction and Granger causality estimation by experimental data are described in this article. The EEG is written down from the brain of WAG/Rij rats, which are absence-epilepsy contaminated. The EEG episodes well enough described in terms of small order linear display along with the episodes with expressed nonlinearity are revealed during the analysis. The EEG episodes ordering is spent in accordance with the model parameters received and physio-logical condition of the animals.

Hypermultistability in laser’s models with large delay

We study model of monomode semiconductor laser with optoelectronic feedback, based on balanced equations with delay. We built sets of quasinormal forms in neighboorghood of bifurcation values. The possibility of coexistence of large amount of stable oscillating solutions is shown

Bifurcations in the problem of thermal convection of viscoelastic fluid in a closed cavity with free boundaries heated from below

Bifurcations in the problem of thermal convection of viscoelastic fluid in a square cavity with free boundaries heated from below are studied. General Odroyd model is used for the description of rheological behaviour of the fluid. In the frame of weakly­nonlinear analysis explicit formula is obtained for the boundary separating the rheological parameter space into domains with different type of bifurcations (super­ and subcritical).