Detection of weak directional coupling: phase-dynamics approach versus state-space approach

Area of Science:

• Nonlinear dynamics
• Time series analysis
• Coupled systems

Background:

• Detecting directional couplings in oscillatory systems is crucial for understanding complex interactions.
• Existing methods often focus on phase dynamics or state space interdependencies.

Purpose of the Study:

• To compare the sensitivity and robustness of two distinct methods for detecting weak directional couplings.
• To evaluate performance across varying system similarities, phase diffusion, noise levels, and time series lengths.

Main Methods:

• Analysis of phase dynamics of coupled oscillatory systems.
• Testing for interdependencies in reconstructed state spaces.
• Numerical experiments with varying coupling strengths and system properties.

Main Results:

• Both phase dynamics analysis and state space interdependency testing showed sensitivity to weak couplings.
• Performance varied depending on system similarity, phase diffusion, noise, and data length.
• No single method demonstrated consistent superiority across all tested conditions.

Conclusions:

• A combination of phase dynamics analysis and state space interdependency testing is recommended for comprehensive and reliable characterization of coupled systems.
• The choice of method may depend on specific characteristics of the systems under investigation.