Causal interactions in dynamical systems

Abstract

Nonlinear Systems Classically, causality requires that state A has independent information that influences state B. If this happens only in one direction, A is said to causally act on B. In nonlinear dynamical systems, however, interactions are mutual. Their parts cannot be separated in this simple way. A definition of causal efficacy that generalizes the classical unidirectional (“acyclic”) notion of causality to the nonseparable bidirectional (“cyclic”) case is missing. Harnack et al. propose a mathematically transparent definition of effective causal influences in cyclic dynamical systems. This relies on reconstructions of the system's overall state from measurements. Reconstructions are obtained in parallel from observations at different system components. Although generally the respective reconstructions are topologically equivalent, the mapping among the reconstructions exhibits distortions that reflect effective causal influences. Phys. Rev. Lett. 119 , 098301 (2017).