A novel method to identify the scaling region for chaotic time series correlation dimension calculation

To obtain more accurate correlation dimension estimations for chaotic time series, a novel scaling region identification method is developed. First, points that obviously do not belong to the scaling region associated with the whole double logarithm correlation integral curve are removed using the K-means algorithm. Second, a point-slope-error algorithm is developed to recognize a possible scaling region. Third, the K-means algorithm is used again to further remove a small interval of interfering points in the possible scaling region to obtain a more precise scaling region. The correlation dimension of four typical chaotic attractors and five curves generated by the Weierstrass-Mandelbrot fractal function were calculated using the proposed method. These calculated values were very close to the respective theoretical fractal dimensions. Moreover, the effectiveness of our method in identifying the scaling region was compared with existing methods. Results show that our method can distinguish the scaling region objectively, accurately, automatically and quickly, making estimations of the correlation dimension more precise and affording significant improvements in nonlinear analysis.

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