On Causality in Dynamical Systems

TL;DR

This paper introduces a new analytical method to identify causal influences in complex dynamical systems, especially nonseparable ones, using pairs of measurements, applicable to various types of systems.

Contribution

It provides a mathematically tractable definition of gradual causality for nonseparable dynamical systems and a method for determining directed influences from time series data.

Findings

Method successfully applied to coupled differential equations.

Effective in analyzing linear stochastic systems.

Fulfills basic causality measure requirements.

Abstract

Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical definition of gradual causal interaction is still lacking for nonseparable dynamical systems. The solution proposed here is analytically tractable for time discrete chaotic maps and is shown to fulfill basic requirements for causality measures. It implies a method for determination of directed effective influences using pairs of measurements from dynamical systems. Applications to time series from systems of coupled differential equations and linear stochastic systems demonstrate its general utility.