Journal in journal

The article discusses the method of analysis and automatic diagnostics of the characteristics of various components of complex signals on digital data on the basis of continuous wavelet transformation. The results of processing of experimental data are exposed. The article shows that the offered method of single­channel continuous wavelet transformation with the subsequent analysis of instantaneous transformation energy in a certain frequency band allows tracing a zone of the registered high­intensity waves of sound and superficial type in an automatic mode.

The dynamics of coupled maps’ ensembles is investigated in the context of description of spatio­temporal processes in the myocardium. Particular, the dynamics of two coupled maps is explored as well as modeling the interaction of pacemaker (oscillatory) cell and myocyte (excitable cell), and the interation of two pacemakers.

New computationally efficient model of cardiac activity is introduced. The model is a four­dimensional map based on well­known Luo–Rudy model. Capabilities of the model in replication of the basic cardiac cells’ properties are shown. Analysis of relationship between changes in individual parameters of the model and biophysical processes in real cardiac cells has been made. The model can reproduce two basic activity modes such as excitable and oscillatory regimes. Bifurcation mechanisms of transitions of between these regimes are investigated using phase space analysis.

All symmetry related invariant manifolds, admitting localized vibrations, for dynamical models on plane square lattice were found by group­theoretical methods. Discrete breathers were constructed on these manifolds for the model with homogeneous potentials of interparticle interactions and their stability was studied. Nontrivial breather solutions which are not nonlinear normal modes by Rosenberg have been revealed for the above model despite it admits space­time separation of dynamical variables.

Nonlinear dynamics of the ensemble consisting of three phase­locked generators, which are coupled in a ring, is discovered. By force of computational modeling, which is based on the theory of oscillations, the regimes of the generators collective behavior is examined; the districts of synchronous and quasi­synchronous regimes are distinguished in the parameter space; the restructuring of the dynamics behavior on the boards of the distinguished districts is analyzed.

In this paper the results of the study of the intermittent behavior taking place near the phase synchronization boundary on the different time scales of the observation are given. It has been shown that below the phase synchronization boundary, in the area of eyelet intermittency there are time scales where the ring intermittency is also observed. In other words, for the certain values of the coupling strength and time scale of observation both types of the intermittent behavior take place simultaneously. In this paper the theory of this type of the intermittent behavior is developed.

In the article we present an overview of a number of continuous wavelet transform­based techniques for analysis and diagnostic of oscillatory neuronal network activity of brain in experimentally obtained  electroencephalographic data. We describe a technique for automatic detection of characteristic patterns for paroxysmal activity (spike­wave discharges) in epileptic electroencephalogram (EEG) based on wavelet spectrum power analysis, obtained with continuous wavelet transform with complex mother wavelet (Morlet) in specific frequency ranges.

The paper reviews the modern problems of nonlinear physics, where q­breathers theory finds its applications.