Identification of scaling regime in chaotic correlation dimension calculation

Abstract

For many chaotic systems, accurate calculation of the correlation dimension by using Grassberger-Procaccia (GP) algorithm is sometimes difficult due to the difficulty in selecting the right scaling regime (i.e. straight line portion) from correlation dimension curves which are often irregular. By now ldquovisual inspectionrdquo is still widely adopted as the method to determine scaling regime, which suffers from the irregularity in correlation dimension curves and may further lead to a bad correlation dimension. So in this paper, a new computer-implemented method for the identification of scaling regime in correlation dimension plots based on K-means clustering algorithm is proposed. The effectiveness of the method is demonstrated by examples based on the data produced by several typical chaotic attractors and the data of a real load time series. Compared with traditional manual selection approach, the proposed approach can deal with the irregular correlation dimension curves more effectively.