Effective detection of coupling in short and noisy bivariate data.

In the study of complex systems, one of the primary concerns is the characterization and quantification of interdependencies between different subsystems. In real-life systems, the nature of dependencies or coupling can be nonlinear and asymmetric, rendering the classical linear methods unsuitable for this purpose. Furthermore, experimental signals are noisy and short, which pose additional constraints for the measurement of underlying coupling. We discuss an index based on nonlinear dynamical system theory to measure the degree of coupling which can be asymmetric. The usefulness of this index has been demonstrated by several examples including simulated and real-life signals. This index is found to effectively disclose the nature and the degree of interactions even when the coupling is very weak and data are noisy and of limited length; by this way, new insight into the functioning of the underlying complex system is possible.