Permutation-information-theory approach to unveil delay dynamics from time-series analysis

Area of Science:

• Complex Systems
• Information Theory
• Nonlinear Dynamics

Background:

• Time delay phenomena are crucial in many dynamical systems.
• Accurate identification of these delays is essential for system analysis and prediction.
• Traditional methods can be sensitive to noise and system complexity.

Purpose of the Study:

• To develop a robust method for identifying time delay phenomena from time series data.
• To utilize information theory quantifiers for reliable time delay estimation.
• To demonstrate the effectiveness of the proposed method on chaotic systems.

Main Methods:

• Employing permutation entropy and permutation statistical complexity as information theory quantifiers.
• Analyzing time series data from the Mackey-Glass equations operating in a chaotic regime.
• Investigating the extrema of quantifiers to identify characteristic time delays.

Main Results:

• Permutation entropy and statistical complexity exhibit clear extrema when the embedding delay matches the system's time delay.
• The proposed method is straightforward to apply and robust against observational and dynamical noise.
• Time delay identification proved more efficient in noisy environments and effective for systems with low feedback or high nonlinearity.

Conclusions:

• Information theory-based quantifiers offer a reliable approach for time delay identification in dynamical systems.
• The permutation approach is a robust and efficient tool for analyzing time-delayed systems, even under challenging conditions.
• This method enhances the understanding and analysis of complex, nonlinear, and noisy time series data.