[Problems in estimating the dimensions of strange attractors in the analysis of biophysical data]

Basic algorithms of calculating the dimensions of strange attractors from experimental data are considered. A special emphasis is placed on difficulties arising when the methods of solution of the reverse nonlinear dynamic problem are used in the analysis of the behavior of biological systems. These difficulties are associated with a poor convergence and weak stability of estimated values as well as a low degree of statistical confidence. Factors that hamper the estimation of strange attractor dimensions with reasonable accuracy are discussed by the example of analysis of human electrocardiograms. A method for the statistcal estimation of dimensions of attractors is proposed based on multidimensional imitational modeling.