Linear And Nonlinear Methods For Dynamical System Correlation Analysis

Abstract

In recent decades different methods have been developed to analyse correlations of complex dynamic systems. In the field of medical tests, there is a growing interest in how the new information can be gained on the interactions between the main physiological regulating mechanisms both in healthy and diseased individuals. Recent advances in dynamic linear, nonlinear and information theory, allowed the study of information flows between causal and non-causal time series using multivariate analysis. To investigate the correlations in and between the main control systems, as well as for the quantification of the interactions between these complex systems a variety of linear and non-linear methods have been proposed up to the present time. In this paper will be presented the most used approaches, both linear and nonlinear, to quantify the direct or indirect correlations and directionality of these interactions (master-slave relationship).