INFLUENCE OF SAMPLING LENGTH AND SAMPLING INTERVAL ON CALCULATING THE FRACTAL DIMENSION OF CHAOTIC ATTRACTORS

Abstract

This paper intends to study the influences of the sampling length and sampling interval of time series on the chaotic attractors' fractal dimension calculation. Four kinds of univariate time-series signals from different chaotic systems were chosen, and then fractal dimensions of attractors under different sampling lengths and sampling intervals were calculated by the method of correlation dimension. The results show clearly that the chaotic attractors' fractal dimension is related to both the sampling length and the sampling interval. With the increase of the sampling length, all attractors' fractal dimensions tend to increase gradually first and then become stable. However, the fractal dimension remains stable only in a suitable range of the sampling interval, in which the attractor of the chaotic system can be reconstructed from one univariate time-series signal; if the sampling interval is unusually large or small, the fractal dimension will be unstable and the reconstructed attractor will be seriously distorted. Therefore, the dimension saturation method and the delay-coordinate's time difference method for determining the sampling length and the sampling interval were proposed separately, which are significant for improving the calculation accuracy for the chaotic attractor's dimension, reflecting the dynamics of complicated systems correctly, saving computational time as well as enhancing the computation efficiency.