An intelligent algorithm to fast and accurately detect chaotic correlation dimension

Abstract

Detecting the complexity of natural systems, such as hydrological systems, can help improve our understanding of complex interactions and feedback between variables in these systems. The correlation dimension method, as one of the most useful methods, has been applied in many studies to investigate the chaos and detect the intrinsic dimensions of underlying dynamic systems. However, this method often relies on manual inspection due to uncertainties from identifying the scaling region, making the correlation dimension value calculation troublesome and subjective. Therefore, it is necessary to propose a fast and intelligent algorithm to solve the above problem. This study implies the distinct windows tracking technique and fuzzy C-means clustering algorithm to accurately identify the scaling range and estimate the correlation dimension values. The proposed method is verified using the classic Lorenz chaotic system and 10 streamflow series in the Daling River basin of Liaoning Province, China. The results reveal that the proposed method is an intelligent and robust method for rapidly and accurately calculating the correlation dimension values, and the average operation efficiency of the proposed algorithm is 30 times faster than that of the original Grassberger-Procaccia algorithm.

Keywords

chaotic time series / correlation dimension / distinct windows tracking / fuzzy C-means clustering

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2025 The Author(s). River published by Wiley-VCH GmbH on behalf of China Institute of Water Resources and Hydropower Research (IWHR).