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Time-varying periodicities are commonly observed in biological time series. In this paper, we discuss three different algorithms to detect and quantify change in periodicity. Each technique uses a sliding window to estimate periodic components in short subseries of a longer recording. The three techniques we utilize are based on: 1) standard Fourier spectral estimation; 2) an information theoretic adaption of linear (autoregressive) modeling; and 3) geometric properties of the embedded time series. We compare the results obtained from each of these methods using artificial data and experimental data from swine ventricular fibrillation (VF). Spectral estimates have previously been applied to VF time series to show a time-dependent trend in the dominant frequency. We confirm this result by showing that the dominant period of VF, following onset, first decreases to a minimum and then rises to a plateau. Furthermore, our algorithms detect longer period correlations which may indicate the presence of additional periodic oscillations or more complex nonlinear structure. We show that in general this possibly nonlinear structure is most apparent immediately after the onset of VF. Index Terms--Description length, linear modeling, periodicity detection, unstable periodic orbits, ventricular fibrillation.

We provide numerical evidence that the electrocardiogram data collected from pigs during induced ventricular fibrillation cannot be described by a monotonic nonlinear transformation of linearly filtered noise. To establish this we use surrogate techniques and apply two test statistics: (1) the Takens' maximum likelihood estimator of the Grassberger-Procaccia correlation dimension and (2) an improved correlation dimension estimation routine. The improved dimension estimates provide evidence that the correlation dimension of the underlying dynamics during the episode of VF in the first 30 s is slightly less than 6. This result is consistent and reproducible among subjects. (c) 2000 American Institute of Physics.

Nonlinear time series analysis is becoming an ever more powerful tool to explore complex phenomena and uncover underlying patterns from irregular data recorded from experiments. However, the existence of dynamical nonstationarity in time series data causes many results of such analysis to be questionable and inconclusive. It is increasingly recognized that detecting dynamical nonstationarity is a crucial precursor to data analysis. In this paper, we present a test procedure to detect dynamical nonstationarity by directly inspecting the dependence of nonlinear statistical distributions on absolute time along a trajectory in phase space. We test this method using a broad range of data, chaotic, stochastic and power-law noise, both computer-generated and observed, and show that it provides a reliable test method in analyzing experimental data. (c) 1999 American Institute of Physics.