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Topological Causality in Dynamical Systems.

Daniel Harnack¹, Erik Laminski¹, Maik Schünemann¹

¹University of Bremen, 28359 Bremen, Germany and Center for Cognitive Science (ZKW), 28359 Bremen, Germany.

Physical Review Letters

|September 27, 2017

Summary

This summary is machine-generated.

This study introduces new causality indices for complex systems. These indices quantify causal influences in cyclic systems, revealing their strength and time-varying nature.

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Area of Science:

Complex Systems Science
Nonlinear Dynamics
Causality Theory

Background:

Determining causal relations is crucial for understanding complex systems.
Classical causality measures fail for nonlinear, inseparable systems.
A transparent measure for causal influences in cyclic systems is needed.

Purpose of the Study:

Develop a mathematically sound measure for effective causal influences in cyclic deterministic systems.
Quantify the magnitude and temporal dynamics of causal links.
Address limitations of classical causality in nonlinear contexts.

Main Methods:

Utilized time-delay state space reconstructions from observable time series.
Analyzed expansions of mappings between reconstructed state spaces.
Defined novel causality indices based on these expansions.

Main Results:

The method reveals directed coupling strengths and state-dependent influences.
Novel causality indices accurately capture asymmetry and time-dependence.
Effective strengths of causal links in complex systems are measurable.

Conclusions:

The proposed causality indices offer a transparent and effective way to measure causal influences in cyclic systems.
This approach overcomes limitations of classical causality in nonlinear dynamics.
Provides a powerful tool for analyzing complex systems across scientific disciplines.