The theoretical ground of the method for defining a geometric characteristic as minimal attractor embedding dimension m_o on the basis of matrix decomposition for different thapes of dynamical systems is proposed. On the subset of chaotic attractor in Euclidean space R~m a function z(m) is constructed. It defines a measure of topological instability of the attractor when enlarging state space dimension (R~m → R~(m+1)). The value of z(m) changes monotonously when enlarging m, but if m ≥ m_0, then z(m) does not depend on m. The computer confirmation of the theoretical results is presented. The investigation of digital electrocardiosignals using local-topological analysis of chaotic attractor trajectories is carried out.
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