Review of Actual Problems of Nonlinear Dynamics

Signals obtained from most of real­world systems, especially from living organisms, are irregular, often chaotic, non­stationary, and noise­corrupted. Since modern measuring devices usually realize digital processing of information, recordings of the signals take the form of a discrete sequence of samples (a time series). The present paper gives a brief overview of the possibilities of such experimental data processing based on reconstruction and usage of a predictive empirical model of a time realization under study.

Different universal methods of calculation of index of chaotic synchronization are considered. One of the methods, which is based on mutual coherence function, is presented in more detail. Its advantages and disadvantages, sensibility to external noise and distortions are discussed. Application of the algorithm to process of destruction of complete chaotic synchronization in two coupled systems with discrete time are demonstrated.

This work is devoted to the intermittent behavior caused by the interplay between the dynamical mechanisms resulting in the type­I intermittency and the stochastic processes. The analytical consideration of the laminar phase distribution is given.

Spatial coherence of an optical field in a direction of its propagation depending on parameters of frequency and angular spectra of the field is considered. The expressions for function and length of longitudinal coherence are derived depending on width of frequency and angular spectra. The competing influence of angular and frequency spectra of a field on its longitudinal coherence is discussed. The experimental study with use the Michelson interferometer of longitudinal shift confirming theoretical results are executed.

In the present review we summarize the known informations about the evolution of a strongly nonequilibrium quasiparticle electron­positron plasma created from the vacuum under the influence of a strong nonstationary electromagnetic field. The methodical basis is given by quantum kinetic equations of the non­Markovian type which are nonperturbative consequences of the basic equations of QED in the collisionless approximation.

The modern knowledges of bifurcations of dynamical systems in the presence of noise are presenred. The main definitions are given and certain typical examples of the bifurcations in the presence of additive and multiplicative noise are considered.

The presented paper is an analytical review of the methods and examples of applications of the continuous and discrete wavelet transform in geophysical study. The possibility of the extension of application of the wavelet­based methods in geophysics is also considered.

This review is devoted to the famous Dutch scientist Balthasar van der Pol, who made a significant contribution to the development of radio­engineering, physics and mathematics. The review outlines only one essential point of his work, associated with the equation that bears his  name, and has a surprisingly wide range of applications in natural sciences. In this review we discuss the following matters.

• The biography of van der Pol, history of his equation and supposed precursors.

• The contribution of A.A. Andronov in the theory of self­oscillations.

We review the results of studies of spontaneous and stimulated emission of relativistic particles in natural and photonic crystals.We consider the diffraction of electromagnetic waves in a crystal, and the resonance and parametric (quasi-Cherenkov) X-ray radiation, the radiation in the channeling of relativistic particles in crystals, diffraction radiation in conditions of channeling, diffraction radiation of a relativistic oscillator, induced radiation in multidimensional space-periodic resonators (natural or artificial (electromagnetic, photonic) crystals).

The role of the discrete description of electron-wave interaction in high-power traveling wave tubes is shown. Deals with the development of this trend on the basis of the theory of interaction of the difference equation excitation waveguides. The validity of the linear theory and developed a universal characteristic equation of electron waves, using the difference equation excitation waveguides in stopbands of slow-wave systems.