Matrix analysis
Information and Self-Organization: A Macroscopic Approach to Complex Systems (Springer Series in Synergetics)
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The theoretical ground of the method for defining a geometric characteristic as minimal attractor embedding dimension m0 on the basis of matrix decomposition for different types of dynamical systems is proposed. On the subset of chaotic attractor in Euclidean space Rm a function z(m) is constructed. It defines a measure of topological instability of the attractor when enlarging state space dimension (Rm → Rm+1). The value of z(m) changes monotonously when enlarging m, but if m, ≤ m0 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.