# Topological Causality in Dynamical Systems.

@article{Harnack2017TopologicalCI, title={Topological Causality in Dynamical Systems.}, author={Daniel Harnack and Erik Laminski and Maik Sch{\"u}nemann and Klaus R. Pawelzik}, journal={Physical review letters}, year={2017}, volume={119 9}, pages={ 098301 } }

Determination of causal relations among observables is of fundamental interest in many fields dealing with complex systems. Since nonlinear systems generically behave as wholes, classical notions of causality assuming separability of subsystems often turn out inadequate. Still lacking is a mathematically transparent measure of the magnitude of effective causal influences in cyclic systems. For deterministic systems we found that the expansions of mappings among time-delay state space…

## 26 Citations

Reliable Detection of Causal Influences in Dynamical Systems

- Computer Science
- 2020

The proposed method exploits local inflations of manifolds to obtain estimates of upper bounds on the information loss among state reconstructions from two observables and comes with a test for the absence of causal influences.

Exact Inference of Causal Relations in Dynamical Systems

- Computer Science
- 2018

A new method is presented, which distinguishes and assigns probabilities to the presence of all the possible causal relations between two or more time series from dynamical systems and is validated on synthetic datasets and applied to EEG data recorded in epileptic patients.

Complete Inference of Causal Relations between Dynamical Systems.

- Computer Science
- 2020

A new method is presented, which distinguishes and assigns probabilities to the presence of all the possible causal relations between two or more time series from dynamical systems and is validated on synthetic datasets and applied to EEG data recorded in epileptic patients.

Reliable Detection of Causal Asymmetries in Dynamical Systems

- Computer Science
- 2020

The proposed method exploits local inflations of manifolds to obtain estimates of upper bounds on the information loss among state reconstructions from two observables and comes with a test for the absence of causal influences.

Transient and equilibrium causal effects in coupled oscillators.

- MathematicsChaos
- 2018

Relationships between the two kinds of causal effects are found for unidirectionally coupled stochastic linear oscillators depending on their frequencies and damping factors and their practical applicability to extracting equilibrium causal effects from time series is argued.

Partial cross mapping eliminates indirect causal influences

- Computer ScienceNature Communications
- 2020

A data-driven model-independent method to distinguish direct from indirect causality and test its applicability to real-world data, which is expected to be indispensable in unlocking and deciphering the inner mechanisms of real systems in diverse disciplines from data.

Causation Inference and Information Flow in Dynamical Systems : Theory and Applications

- Computer Science
- 2018

Questions of causation are foundational across science and often relate further to problems of control, policy decisions, and forecasts, as well as several topical applications, which this Focus Issue considers.

Continuity Scaling: A Rigorous Framework for Detecting and Quantifying Causality Accurately

- Materials ScienceResearch
- 2022

Data-based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering, and beyond. Inspired by the widely used methodology in…

Detecting directional couplings from multivariate flows by the joint distance distribution.

- Computer ScienceChaos
- 2018

The method of the joint distance distribution to detect directional couplings between two multivariate flows is re-examine, based on the forced Takens theorem, and it is shown that this method outperforms the lowest dimensional transfer entropy in the cases considered.

Introduction to Focus Issue: Causation inference and information flow in dynamical systems: Theory and applications.

- Computer ScienceChaos
- 2018

Questions of causation are foundational across science and often relate further to problems of control, policy decisions, and forecasts, as well as to several topical applications.

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