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

Обзоры актуальных проблем нелинейной динамики

Longitudinal coherence of optical field

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.

Distribution of the laminar phases in the case of type­i intermittency with noise

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.

Methods of measuring chaotic synchronization

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.

Modeling from time series and applications to processing of complex signals

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.

Multifractal analysis of digital images

The article is based on the lecture that was given by the first author at the school StatInfo­2009. In the first part the microcanonical variant of multifractal formalism is reviewed. Possibilities for digital image analysis and reconstruction are discussed at the level of technical strictness.

Wavelet-­analysis and examples of its applications

Theoretical background of the wavelet­analysis and a series of applications of the given method are considered including a study of clustering phenomena for synchronous dynamics in structural units if the kidney, tactile information encoding by neurons of the trigeminal complex and detection of information messages from the chaotic carrying signal.

Unique properties of open cavities and wavegiudes containing layered metamaterial

The review of works on studying arti?cial media with negative refractive index and  their unique application is given. We make a point of negative refraction and lens e?ects in plan-parallel  layers of such metamaterials. The properties and stability conditions of waveguide modes in  layered structures and open cavities are considered in terms of the e?ective di?raction and  dispersion lengths.

Development and improvement of field emitters containing carbon materials

Achievements and problems in creation of ?eld emitters for vacuum microwave devices are described. The main attention is devoted to the emitters made of containing carbon materials for  high-voltage devices operating at technical vacuum conditions 10?6–10?8 Torr. The brief review of existing works is presented. Results of investigations performed in SPbSPU are described.

Theory of waveguides excitation

The theory of waveguide excitation is presented, based on expansions of the electromagnetic ?eld by proper waves of waveguide. Necessary properties of smooth and periodic waveguides, including the conditions of orthogonality of plane and the volume of the waveguide are given. Main properties of pseudo-periodic waveguides are described. Thisis a new class of waveguide systems. Di?erent forms of the waveguides-excitation theory are considered.

Chaos and nonintegrability in hamiltonian systems

The article is devoted to historical development of one key aspect of Hamiltonian systems – nonintegrability, and its relation with chaotic behavior of the system. Evolution from the concept of quite integrable system to partly integrable one is shown. The relation of nonintegrability with such fundamental concepts as Kolmogorov stability, systems with divided phase space, Arnold di?usion, Zaslavsky web and others is discussed.