ABSTRACT
Nonlinear time series analysis is a practical spinoff from complex dynamical systems theory and chaos theory. It allows one to characterize dynamical systems in which nonlinearities give rise to a complex temporal evolution. Importantly, this concept allows extracting information that cannot be resolved using classical linear techniques such as the power spectrum or spectral coherence. Applications of nonlinear time series analysis to signals measured from the brain contribute to our understanding of brain functions and malfunctions and thereby help to advance cognitive neuroscience and neurology. In this chapter, we show how a combination of a nonlinear prediction error and the Monte Carlo concept of surrogate time series can be used to attempt to distinguish between purely stochastic, purely deterministic, and deterministic dynamics superimposed with noise.
