Local noise sensitivity: Insight into the noise effect on chaotic dynamics

Area of Science:

• Nonlinear Dynamics
• Time Series Analysis
• Chaos Theory

Background:

• Noise contamination is a major challenge in analyzing chaotic experimental data.
• Understanding noise-nonlinear dynamics interactions is crucial for advancing nonlinear time series analysis.
• Existing methods struggle with noise, limiting the application of chaotic dynamics analysis.

Purpose of the Study:

• To analyze the local effects of noise on chaotic dynamics with smooth attractors.
• To investigate the phenomenon of local noise sensitivity.
• To assess if reconstructed dynamics can represent local noise sensitivity.

Main Methods:

• Calculation of local translation errors using the Wayland test.
• Application to noise-induced Lorenz and Rössler chaotic models.
• Analysis of experimental green light photoplethysmogram data.

Main Results:

• Identified local regions of high local translation error on chaotic attractors under noise induction.
• Defined this phenomenon as local noise sensitivity.
• Found local noise-sensitive regions near system equilibrium points in models.
• Demonstrated that reconstructed dynamics accurately reflect local noise sensitivity.

Conclusions:

• Local noise sensitivity is a key phenomenon in noisy chaotic systems.
• Noise-sensitive regions are often located near equilibrium points.
• The concept aids in identifying vulnerable areas in chaotic attractors for applied studies.