Abstract
Correlation dimension (CD) and the largest Lyapunov exponent (LLE), which are two most important nonlinear invariant measures of nonlinear system, are adopted to characterize the complexity and stability of human brain during all sleep stages. In order to find an optimal embedding to reconstruct phase space, the C-C method and Cao's algorithm were thoroughly analyzed and implemented in efficient ways. Additionally, the G-P algorithm and Kantz's algorithm are also implemented for calculation of CD and LLE respectively. Eight normal sleep EEG records are acquired from MIT-BIH sleep- EDF database for this study. The values of CD and LLE for 30s epochs are calculated, and their mean and standard deviation values are evaluated as well. The results indicate that CD and LLE decrease from the waking stage to stages I, II and III-IV, and they have large values during rapid eye movement (REM) sleep stage. Then, a qualitative conclusion may be drawn that during waking stage and REM sleep stage, brain activity has higher complexity and lower stability than during other stages.
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