关键词: 分形, 关联维数, 无标度区, 自动识别

Abstract: The identification of the linear segment in double logarithmic curves（or log-log curves）, also known as scaling region （or non-scale range in some papers）, is important in Grassberger-Procaccia（GP） algorithm. The scaling region is normally determined by experience in classical GP algorithm, which may lead the values of the correlation-dimension to be estimated different from person to person. In GP algorithm, the second-order derivative of log-log curves within the scaling region should be zero or slightly fluctuate near zero because the log-log curves are nearly straight lines in that scaling region. Based on this character of the log-log curves, a new method with clear physical meaning is presented to automatically identify the fractal scaling region. The process of this method is simple and can be realized easily on computer. A time series data of the Lorenz strange attractor are used to test the method. The estimated correlation-dimension of Lorenz attractors based on this method is very close to the theoretical value. The numerical results show that the scaling region can be identified accurately and automatically by this method.

Key words: fractal, correlation dimension, scaling region, automatic identification