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

Applied Problems of Nonlinear Oscillation and Wave Theory

Studies of scale invariant change-over dynamics in the hierarchical model of defects development

Hierarchical model of defect development makes possible the consideration of both ordinary and self-organized criticality from the common viewpoint. Scale invariant critical state in this model is presented by fixed points of a renormalization transformation, connected with lifting to the next level of hierarchy. So stable fixed points of the transformation correspond to the self-organized criticality and unstable points correspond to the ordinary one.

Coherent resonance in klystron oscillators on self-excitation threshold

This work presents experimental results of synchronization of coherent resonance phenomena in cascade klystron oscillator with delayed feedback on self-excitation threshold. Degree of coherence, signal-to-noise ratio and synchronization wideband for single and cascade klystron oscillators were compared.

Spectral components’ behavior in coupled pierce diodes near the phase synchronization boundary

In this article we study the dynamics of two unidirectionally coupled Pierce diodes near the phase synchronization boundary in terms of synchronization of spectral components. We show that systems under consideration demonstrate self-similar behavior with any value of coupling strength within the region of our study. The results correlate with the data of the similar research for Rossler systems and circle map. 

Method for calculation of lyapunov exponents spectrum from data series

The new method for the calculating of the spectrum of the Lyapunov exponents from data series is proposed. The already known methods of the same thematic are investigated. The Roessler system is given as an example for describing the proposed method. The results of numerical modeling are presented.

Relationship of generalized and phase synchronization in two unidirectionally coupled chaotic oscillators

The behavior of the boundary of generalized synchronization in two unidirectionally coupled chaotic oscillators depending on the value of the control parameter mismatch between interacting systems has been studied. Peculiarities in its behavior in the field of the relatively large values of the control parameter mistuning have been found. The character of this behavior and physical mechanisms resulting in the generalized synchronization regime onset in such systems have been explained by the analysis of the spectral compound of signal from response system.

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.

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