Information transfer from causal history in complex system dynamics

Area of Science:

• Complex Systems Science
• Information Theory
• Time Series Analysis

Background:

• Understanding temporal dependencies in multivariate systems is crucial.
• Quantifying information flow from historical data to present states remains a challenge.

Purpose of the Study:

• To develop novel information theoretic metrics for quantifying causal history.
• To partition causal history into immediate and distant components, including self- and cross-feedbacks.
• To analyze complex interdependencies in dynamic systems.

Main Methods:

• Developed information theoretic metrics for causal history.
• Partitioned causal history into immediate and distant components.
• Employed Markov property for directed acyclic time-series graphs for efficient estimation.
• Revealed an information aggregation property.

Main Results:

• Demonstrated characterization of memory dependency in synthetic and chaotic systems (Lorenz model).
• Compared memory dependencies of long-memory processes.
• Illustrated sustained complex dynamics through interactive self- and cross-dependencies.

Conclusions:

• The proposed metrics offer a powerful new way to analyze complex interdependencies.
• The information aggregation property highlights how past dynamics accumulate influence.
• This framework advances the understanding of information transfer in dynamic systems.