New systems-analytical approaches to nonlinear coordination

The approaches presented in this article to analyzing nonlinear dynamics in multivariate data (interacting quantities) may help to uncover new insights into the physiological functional organization by considering mechanisms of particular nonlinear coordinated behavior. The systems-analytical approaches are demonstrated with regard to different aspects of the cardiorespiratory and cardiovascular interactions, which are: couplings between respiratory movements and heart-rate fluctuations; couplings between heartbeats and respiratory rhythms; and couplings between cardiorespiratorily related generators in the brain stem. A representative overview of experimental-mathematical techniques applied to nonlinear coordinations includes the following approaches: isofunctional mathematical modeling and simulation; and analysis of measured experimental bivariate data including multivariate phase-space sets, surrogate data, mutual information, phase synchronizations and bicoherence.