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1 Centre for Applied Dynamics and Optimization, Department of Mathematics, University of Western Australia, Nedlands, Western Australia 6907; and 2 Department of Respiratory Medicine, Princess Margaret Hospital for Children, Subiaco, Western Australia 6008, Australia
We describe an analysis of dynamic behavior apparent in times-series recordings of infant breathing during sleep. Three principal techniques were used: estimation of correlation dimension, surrogate data analysis, and reduced linear (autoregressive) modeling (RARM). Correlation dimension can be used to quantify the complexity of time series and has been applied to a variety of physiological and biological measurements. However, the methods most commonly used to estimate correlation dimension suffer from some technical problems that can produce misleading results if not correctly applied. We used a new technique of estimating correlation dimension that has fewer problems. We tested the significance of dimension estimates by comparing estimates with artificial data sets (surrogate data). On the basis of the analysis, we conclude that the dynamics of infant breathing during quiet sleep can best be described as a nonlinear dynamic system with large-scale, low-dimensional and small-scale, high-dimensional behavior; more specifically, a noise-driven nonlinear system with a two-dimensional periodic orbit. Using our RARM technique, we identified the second period as cyclic amplitude modulation of the same period as periodic breathing. We conclude that our data are consistent with respiration being chaotic.
control of breathing; periodic breathing; dynamical systems; chaos; surrogate data techniques
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