Robust measure for characterizing generalized synchronization

Generalized synchronization between two coupled systems can be characterized by recently proposed interdependency measures calculated from two simultaneously observed time series from them. However, numerical tests have shown that these measures cannot consistently indicate the direction of the coupling for strongly coupled systems or in situations with a large phase space neighbor size. An interdependency measure is proposed here quantifying how close a conditional neighbor is to a true neighbor in terms of the degree of alignment of their principal axes. Numerical tests are carried out on time series generated from a coupled Hénon map and a Lorenz model driven by a Rossler model. Given that a driving system is more dependent on a response system, the results show that the direction of the coupling is consistently detected by using the proposed measure even in those unfavorable cases for the measures mentioned above.