Topological Causality in Dynamical Systems

Daniel Harnack, Erik Laminski, Maik Schünemann, and Klaus Richard Pawelzik
Phys. Rev. Lett. 119, 098301 – Published 1 September 2017
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Abstract

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 reconstructions from different observables not only reflect the directed coupling strengths, but also the dependency of effective influences on the system’s temporally varying state. Estimation of the expansions from pairs of time series is straightforward and used to define novel causality indices. Mathematical and numerical analysis demonstrate that they reveal the asymmetry of causal influences including their time dependence, as well as provide measures for the effective strengths of causal links in complex systems.

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  • Received 10 April 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.098301

© 2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Nonlinear Dynamics

Authors & Affiliations

Daniel Harnack*, Erik Laminski, Maik Schünemann, and Klaus Richard Pawelzik§

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

  • *daniel@neuro.uni-bremen.de
  • e.laminski@uni-bremen.de
  • mschuene@uni-bremen.de
  • §pawelzik@neuro.uni-bremen.de

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Issue

Vol. 119, Iss. 9 — 1 September 2017

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