Applied Problems of Nonlinear Oscillation and Wave Theory

The multiplicative noise influence on the self­sustained oscillatory medium near the oscillation threshold is studied. The chain of the identical quasi­harmonic self­sustained oscillators with the periodic boundary conditions is taken as a simplest model of the oscillatory medium. The parameters of the oscillators are modulated with the white Gaussian noise. The stochastic bifurcations are analyzed for the cases of homogenous and spatially­nonhomogenous noise.

Dynamical modes and nonlinear phenomena in the models of oscillatory system with frequency-phase control in the case of periodic nonlinear characteristics of frequency discriminator are investigated. Stability of synchronous mode is analyzed. The existences of a great number various periodic and chaotic nonsynchronous modes are established. Peculiarities of the system dynamics caused by parameters of frequency control loop are considered. The results are presented in the form of one- and two-parameter bifurcation diagrams, phase portraits, Poincare sections and waveforms of attractors.

The paper examines the impact of the slow movements to effective values of dissipative forces in the equations of fast motion of oscillatory system. It was previously shown that the dissipative characteristics obtained experimentally under harmonic oscillations can change significantly with polyharmonic excitation. In this paper the problem is considered in more detail in relation to the determination of the resonance amplitudes and threshold conditions for parametric and subharmonic resonances.

The paper presents the results of research is carried out in the Institute of Applied Physics and is aimed at creating a CW submillimeter gyrotrons with an output power of several tens of watts. Results of experiments on the 258 GHz gyrotron at the second harmonic of the gyrofrequency are presented. In the course of experiments maximum output power of 200 W and the relative stability of the output frequency at 5 · 10−6 for the hours-long continuous operation of the gyrotron were achieved.

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.

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.

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 R ¨ossler systems and circle map.

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.

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 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, two-parametric bifurcation diagrams and phase portraits. Possible types of motion in driven system are discussed.