Testing whether two chaotic one dimensional processes are dynamically identical

Area of Science:

• Nonlinear dynamics
• Chaos theory
• Experimental physics

Background:

• Chaotic physical processes can be observed through various measurable variables.
• Reconstructing phase-space maps from different time series may yield distinct representations.
• Hypothesizing that these distinct maps originate from the same underlying chaotic system is a common challenge.

Purpose of the Study:

• To introduce a novel method for testing the consistency of reconstructed maps.
• To determine if disparate time-series measurements represent the same chaotic physical process.
• To validate the proposed method using experimental data.

Main Methods:

• Reconstruction of phase-space maps using delay coordinates from time-series data.
• Development of a consistency test for one-dimensional reconstructed maps.
• Application of the method to experimental data from an electric circuit.

Main Results:

• The study presents a method to assess map consistency.
• The method is demonstrated to be applicable to experimental data.
• The effectiveness of the technique in validating the origin of chaotic signals is shown.

Conclusions:

• The introduced method provides a quantitative approach to test if different measurements stem from the same chaotic system.
• This technique is valuable for analyzing and comparing data from various observational perspectives.
• The findings contribute to a deeper understanding of characterizing chaotic dynamics from limited data.