Closeness-centrality-correlation for detecting interdependency between coupled systems

Abstract

Generalized synchronization is a common interdependency between coupled systems which exists in many branches of life, social and physical science. In this paper, a novel method, called closeness-centrality-correlation is proposed for the detection of this interdependency. The proposed method is based on a global network measure (i.e., closeness centrality) of recurrence networks resulting from time series. We illustrate the feasibility of the proposed method using a paradigmatic coupled model and compare its performance to other commonly used interdependency methods. The numerical results show that the proposed method is quite satisfactory for detecting interdependency and outperforms the existing joint probability of recurrence method especially for the case that the dynamics of the two coupled subsystems are significantly different. Moreover, through analyzing the time series contaminated by white noise, we demonstrate that our method is robust against white noise. Finally, an application to recorded electroencephalogram data shows that the proposed measure is more reliable to detect the transitions of the interdependencies among the noisy electroencephalogram time series and thus provides longer pre-warning time for the onset of epilepsy.