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

4th National Meeting in Chaos, Complex System and Time Series

La Torre, F Cervantes-De^1 ; González-Trejo, J.I.^1 ; Real-Ramírez, C.A.^1 ; Hoyos-Reyes, L.F.^1

Departamento de Sistemas, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180, Delegacion Azcapotzalco, C.P. 02200, Mexico. D.F., Mexico^1

关键词: Disturbance storm time (Dst);    Geomagnetic activities;    Geometrical structure;    Global indicators;    Higuchi's algorithms;    Nonlinear time series;    Rescaled range analysis;    Self-organized critical;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/475/1/012002/pdf
DOI  :  10.1088/1742-6596/475/1/012002

来源: IOP

【 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.