A new method on solving correlation dimension of chaotic time-series

Traditional G-P algorithm exist two drawbacks in solving the correlation dimension of chaotic time series. The one is the subjective existence to determine scaleless range, the other is calculation error is large when the amount of data is small. For two shortcomings, the fuzzy C-means clustering is introduced to the G-P algorithm to determine the no-scales range. Least-squares fitting method is used to find the saturation correlation dimension value in determining the scalelesss range. Using different amount of Loren and Rossler data, such as 500, 1000, 2000, 5000 and 10000, verify the improved algorithm in this paper. Simulation results show that the error relatively small if the delay time is small when the amount of 500, 1000 and 2000. With the length of data increases, the cluster centre value of the slope relatively flat closer to their ideal value. The conclusions are applicable to Lorenz and Rossler data.