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Lyapunov Exponent and Surrogation Analysis of Patterns of Variability



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Motor Control 2010 14 126 142 2010 Human Kinetics Inc Lyapunov Exponent and Surrogation Analysis of Patterns of Variability Profiles in New Walkers With and Without Down Syndrome Beth A Smith Nick Stergiou and Beverly D Ulrich In previous studies we found that preadolescents with Down syndrome DS produce higher amounts of variability Smith et al 2007 and larger Lyapunov exponent LyE values indicating more instability during walking than their peers with typical development TD Buzzi Ulrich 2004 Here we use nonlinear methods to examine the patterns that characterize gait variability as it emerges in toddlers with TD and with DS rather than after years of practice We calculated Lyapunov exponent LyE values to assess stability of leg trajectories We also tested the use of 3 algorithms for surrogation analysis to investigate mathematical periodicity of toddlers strides Results show that toddlers LyE values were not different between groups or with practice and strides of both groups become more periodic with practice The underlying control strategies are not different between groups at this point in developmental time although control strategies do diverge between the groups by preadolescence Keywords gait nonlinear analysis developmental disabilities Movement scientists have a long history of using linear methods to analyze movement variability Linear tools focus on the magnitude of variability and assume each repetition of a behavior such as a step is independent from those preceding and following Nonlinear methods in contrast focus on the structure of variability by examining patterns in the variability across time and are designed to reveal how one movement influences the next Both the magnitude and structure of variability during movement can differ between persons and each reflects a different characteristic of the performance Stergiou Harbourne Cavanaugh 2006 Sosnoff Newell 2006 Within a specific magnitude of variability differences in structure may exist This is



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