L.A. Manilo, E.P. Zozulya

The time sequence with chaotic properties has complex dynamics peculiar to casual process, at the same time it can be described as a small number of the differential equations. The mathematical apparatus and the methods of research directed on the analysis of chaotic dynamics of behaviour can be used for the description of such signals. Recently the theory of nonlinear dynamic systems and its appendix in various practical areas, including medical researches actively develops. In particular, there were the interesting scientific works based on using of methods of nonlinear dynamics in problems of the analysis of a heart rhythm. Recently in practical problems one of the determined chaos mathematical apparatus methods was extended, namely, the analysis of correlation dimension used for the purpose of estimation of degree of a chaotic time sequence In the present work correlation dimension was calculated as the characteristic of attractor on the algorithm offered Grassberger and Procaccia which was one of the most popular and effective ways of the analysis of time series. According to this method procedure of reconstruction of phase space and restoration attractor of systems is reduced to construction of pseudo-attractor in which vector components are the elements of analyzed sequence chosen with some time delay. The algorithm of calculation of correlation dimension has been realised in system MATLAB and tested on modelling signals and sample of the real data. Results of experiments on modelling signals show that the realised algorithm allows to receive an authentic estimation of correlation dimension with which it is possible to distinguish the determined chaos from casual process. The analysis of correlation dimension of the real data - a signal of a heart rhythm has been carried out in our work at some kinds of arrhythmia. First of all, it is atrial fibrillation which is characterised by frequent and irregular excitation of fibres of a myocardium of auricles. The analysis of sequence RR-intervals carried out by us has shown that dependence of correlation dimension on embedding dimension, has saturation at level of fractional size. It testifies to the chaotic determined nature of a heart rhythm at atrial fibrillation.