Learning driver-response relationships from synchronization patterns

We test recent claims that causal (driver-response) relationships can be deduced from interdependencies between simultaneously measured time series. We apply two recently proposed interdependence measures that should give results similar to cross predictabilities used by previous authors. The systems that we study are asymmetrically coupled simple models (Lorenz, Roessler, and Hénon models), the couplings being such that they lead to generalized synchronization. If the data were perfect (noise-free, infinitely long), we should be able to detect, at least in some cases, which of the coupled systems is the driver and which the response. This might no longer be true if the time series has finite length. Instead, estimated interdependencies depend strongly on which of the systems has a higher effective dimension at the typical neighborhood sizes used to estimate them, and causal relationships are more difficult to detect. We also show that slightly different variants of the interdependence measure can have quite different sensitivities.