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

Прикладные задачи нелинейной теории колебаний и волн

The modes of genetic structure and population size dynamics in evolution model of two­aged population

The modes of genetic structure and size dynamics of structured population are investigated in this work. The reproductive potential and survival rate of reproductive part of population in following years of life are determined on genetic level.

Reconstruction of neutral time-delay systems

The methods are proposed for the reconstruction of time-delay systems modeled by neutral  delay-di?erential equations from their time series. The methods are successfully applied to the recovery of generalized Mackey–Glass equation and equations modeling ship rolling and human movement from simulated data.

Synchronization of klystron oscillator with delayed feedback in the presence of noise

This work presents experimental results of synchronization of klystron oscillator with delayed feedback in the presence of noise. It was shown, that synchronization e?ect signi?cantly decreases noise level, leads to amplifying of synchronizing signal and shortening of synchronization wideband. When additive sum of harmonic and noise signal are directed to klystron input, signal-to-noise ratio signi?cantly increases due to synchronization.

Modelling of dynamic processes with piecewise linear characteristics

Some problems of modelling of dynamic systems with piecewise linear characteristics are considered. New methods of approximation of the piecewise linear functions, in particular, step functions without disadvantages of the traditional Fourier series expansions are suggested. Some questions of convergence and error estimation of the approximation are explored.

Dynamics of the fitzhugh–nagumo system under external periodic force

In paper on basis of radiophysical experiment analysis of dynamics of the FitzHugh–Nagumo system have been carried out. The dependence of oscillation’s regime in the system from force parameter has been found out. In?uence of the form of the external force signal on the system response has been studied.

Stochastic equations and fokker–planck equation for the order parameters in the study of the noise-induced spatial patterns dynamics

From the viewpoint of the order parameters concept spatial pattern formation in excitable ?uctuating medium was researched analytically. The reaction–di?usion system in external noise was considered as a model of such medium. Stochastic equations for the unstable modes amplitudes (order parameters) and the dispersion equations for the average unstable modes amplitudes were received. Fokker–Planck equation for the order parameters was received.

Effect of noise on generalized synchronization of spatially extended systems described by ginzburg–landau equations

E?ect 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 a?ect the synchronous regime threshold in such systems. The reasons of the revealed particularity have been explained by means of the modi?ed system approach and con?rmed by the results of numerical simulation.

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.