Ordinal partition transition network based complexity measures for inferring coupling direction and delay from time...

Area of Science:

• Complex systems science
• Nonlinear dynamics
• Time series analysis

Background:

• Ordinal partition transition networks (OPTNs) offer a novel way to analyze dynamical systems.
• Understanding causal interactions in coupled systems is crucial for scientific discovery.

Purpose of the Study:

• To develop and validate OPTN-based complexity measures for inferring coupling direction between two time series.
• To assess the effectiveness of these measures across different types of dynamical systems.

Main Methods:

• Construction of ordinal partition transition networks (OPTNs) from time series data.
• Development of complexity measures derived from OPTNs to quantify directional interactions.
• Application to simulated data (stochastic processes, chaotic Hénon maps) and real-world climate data.

Main Results:

• Successfully identified interaction delays in unidirectional and bidirectional coupling configurations for stochastic processes.
• Captured causal interactions in coupled chaotic Hénon maps before synchronization across various coupling strengths.
• Revealed interaction delays in real-world climate time series from Oxford and Vienna.

Conclusions:

• OPTN-based complexity measures are effective tools for causal inference in time series analysis.
• The approach provides insights into the dynamics of coupled systems, even in complex real-world scenarios.
• Ordinal partition transition networks offer a robust framework for understanding time series interactions.