Four Methods to Distinguish between Fractal Dimensions in Time Series through Recurrence Quantification Analysis

Area of Science:

• Complex Systems Science
• Nonlinear Dynamics
• Physiology and Human Behavior Analysis

Background:

• Fractal properties are common in human behavior and physiological time series.
• Recurrence quantification analysis (RQA) is a potential method for capturing these properties.
• Existing methods lack the ability to quantify fractal fluctuations using recurrence-based approaches.

Purpose of the Study:

• To propose and test novel recurrence-based methods for quantifying fractal fluctuations.
• To bridge the gap between fractal analysis and recurrence quantification analysis.
• To evaluate the accuracy and applicability of these new methods.

Main Methods:

• Development of several approaches to quantify fractal fluctuations using recurrence-based analysis.
• Utilizing recurrence plots for extracting fractal fluctuation measures.
• Testing methods on both synthetic and empirical time-series data.

Main Results:

• Demonstrated that fractal fluctuations can be extracted using recurrence plots.
• Presented and contrasted different recurrence-based approaches for fractal quantification.
• Evaluated the accuracy and range of applicability of the proposed methods.

Conclusions:

• Recurrence-based methods offer a viable approach for quantifying fractal fluctuations in time series.
• The proposed methods provide new tools for analyzing complex dynamics in various data types.
• Further research can explore the application of these methods in diverse scientific fields.