Symbolic Dynamics, Poincaré Plot Analysis and Compression Entropy Estimate Complexity in Biological Time Series

Methods from nonlinear dynamics have shown new insights into alterations of the cardiovascular system under various physiological and pathological conditions, and thus providing additional prognostic information. In this chapter prominent complexity methods of non-linear dynamics as symbolic dynamics, Poincare plot analyses, and compression entropy are introduced and their algorithmic implementations and application examples in clinical trials are provided. Especially, we will give their basic theoretical background, their main features and demonstrate their usefulness in different applications in the field of cardiovascular and cardiorespiratory time series analyses.