Computing Lyapunov dimension and applying it for geomagnetic indices prediction

The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2018-10-16

A method for computing the Lyapunov dimension from the realization of one variable of a dynamical system is proposed. The equality of the information dimension, the Lyapunov dimension, and capacity dimension is noted. The entropy of the distribution of the norms of the tangent vectors of a dynamical system and the Lyapunov dimension are considered together. Theoretical calculations are accompanied by an example of a numerical calculation of the Lyapunov dimension and the mentioned entropy for time series of geomagnetic Kp, Dst, and AE indices. In the considered indices, the entropy is close to the maximum value, and this leads to the closeness of the Lyapunov dimension to the capacity. A variable structure of the Dst index is noted. Using the example of geomagnetic indices, it is confirmed that the Grassberger-Procaccia correlation dimension is smaller than the Lyapunov dimension.

dynamical system; Lyapunov dimension; manifold; distribution; Lyapunov exponents; geomagnetic indices; info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion

Open access content. Open access content

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System research and information technologies
Russian

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