Determination of Dimension of Embedding for Chaotic Attractors

摘要

We suggested method for solving one of the problems which are urgent for systems with deterministic chaos. Namely, the problem about determination of dimension of their embedding for one known variable represented by point-wise time series. It is assumed that unknown model of an object is an autonomous system of ordinary differential equations. On the basis of analysis of peculiarities of such systems and their attractors we developed the algorithm, which makes it possible to determine uniquely dimension of embedding. We adduced comparison of the suggested approach with the known "false nearest-neighbor" method.