Fractal dimension algorithms and their application to time series associated with natural phenomena

摘要

Chaotic invariants like the fractal dimensions are used to characterize non-linear time series.The fractal dimension is an important characteristic of systems,because it contains information about their geometrical structure at multiple scales.In this work,three algorithms are applied to non-linear time series: spectral analysis,rescaled range analysis and Higuchi's algorithm.The analyzed time series are associated with natural phenomena.The disturbance storm time (Dst) is a global indicator of the state of the Earth's geomagnetic activity.The time series used in this work show a self-similar behavior,which depends on the time scale of measurements.It is also observed that fractal dimensions,D,calculated with Higuchi's method may not be constant over-all time scales.This work shows that during 2001,D reaches its lowest values in March and November.The possibility that D recovers a change pattern arising from self-organized critical phenomena is also discussed.