Detection of synchronization between chaotic signals: An adaptive similarity-based approach

We present an adaptive similarity-based approach to detect generalized synchronization (GS) with n:m phase synchronization (PS), where n and m are integers and one of them is 1. This approach is based on the similarity index (SI) and Gaussian mixture model with the minimum description length criterion. The clustering method, which is shown to be superior to the closeness and connectivity of a continuous function, is employed in this study to detect the existence of GS with n:m PS. We conducted a computer simulation and a finger-lifting experiment to illustrate the effectiveness of the proposed method. In the simulation of a Rössler-Lorenz system, our method outperformed the conventional SI, and GS with 2:1 PS within the coupled system was found. In the experiment of self-paced finger-lifting movement, cortico-muscular GS with 1:2 and 1:3 PS was found between the surface electromyogram signals on the first dorsal interossei muscle and the magnetoencephalographic data in the motor area. The GS with n:m PS (n or m=1) has been simultaneously resolved from both simulation and experiment. The proposed approach thereby provides a promising means for advancing research into both nonlinear dynamics and brain science.