Entropy of weighted recurrence plots.

Area of Science:

• Complexity Science
• Nonlinear Dynamics
• Time Series Analysis

Background:

• Shannon entropy quantifies time series complexity and dynamical regime transitions.
• Recurrence quantification analysis offers alternative complexity measures based on state recurrences.
• Existing recurrence-based entropy definitions can yield inconsistent results.

Purpose of the Study:

• To propose a novel method for quantifying time series complexity using weighted recurrence plots.
• To establish a robust relationship between Shannon entropy derived from weighted recurrence plots and dynamical system properties.
• To validate the proposed method using both simulated and experimental data.

Main Methods:

• Development of a method based on weighted recurrence plots.
• Calculation of Shannon entropy from these weighted recurrence plots.
• Correlation analysis with the largest Lyapunov exponent.

Main Results:

• The Shannon entropy derived from weighted recurrence plots is positively correlated with the largest Lyapunov exponent.
• The proposed method demonstrates its potential on a prototypical dynamical system.
• Successful application to experimental data from a chemical experiment.

Conclusions:

• Weighted recurrence plots provide a reliable basis for calculating Shannon entropy.
• This method offers a consistent and accurate measure of time series complexity.
• The approach is effective for analyzing both theoretical models and real-world experimental data.