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

Applied Problems of Nonlinear Oscillation and Wave Theory

Synchronization of reactively coupled phase oscillators driven by external force

Synchronization of two reactively coupled van der Pol oscillators with external force is investigated in this paper. We consider and compare quasi-periodic motion of oscillators with frequency-locked mode. The paper includes maps of Lyapunov’s exponents, twoparametric bifurcation diagrams and phase portraits. Possible types of motion in driven system are discussed.

Study of chaotic regimes of collective electron dynamics in semiconductor superlattice in external resonator

The paper deals the external resonator effect on collective electron dynamics in the semiconductor superlattice. Numerical simulations have shown that semiconductor superlattice which is characterized by only the regular oscillations in autonomous regime demonstrates chaotic microwave oscillations in the case of interaction with the external electrodynamical system. This phenomena gives a strong potential for novel applications of semiconductor superlattice requiring microwave chaotic signals.

Chaotic microwave pulse train generation in self-oscillatory system based on a ferromagnetic film

Experimental investigations results of the ring self-oscillatory system based on a ferromagnetic film at three-wave interactions were considered. The model describing this system was constructed. The typical regimes of a generation, including generation of the chaotic microwave train were calculated with the help of the constructed model. The numerical simulations and experimental results had a good agreement.

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. 

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 fluctuating medium was researched analytically. The reaction–diffusion 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.

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. Influence of the form of the external force signal on the system response has been studied.

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.

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 effect significantly 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 significantly increases due to synchronization.

Reconstruction of neutral time-delay systems

The methods are proposed for the reconstruction of time-delay systems modeled by neutral delay-differential 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.

The modes of genetic structure and population size dynamics in evolution model of two­-aged 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. It has been shown that evolutional increasing of average population fitness is followed by arising of complicated dynamics of population size and of genetic structure.