ESTIMATING CORRELATION DIMENSIONS OF BIOLOGICAL TIME-SERIES WITH A RELIABLE METHOD

This article deals with a problem on estimating correlation dimensions of possible attractors reconstructed from biological rime series data . The analyzed data are the Jive Japanese vowels, /a/, /i/, /u/, /e/ a nd /o/ and two pulse waves in human finger capillary vessels. The esti mation algorithm used here is not the conventional Grassberger-Procacc ia algorithm, but a new method proposed by Judd, which solves some pro blems intrinsic to the conventional method. To avoid several artifacts that might be involved in the analysis, such as the limited number of time series data, the finite resolution of data points, and the exist ence of the observational noise, the statistical procedure or the meth od of surrogate data is also applied to the real data. As a result, th e existence of strange attractors with fractional dimensions are impli ed in the Japanese vowels /a/ and /o/ Although nonlinearities in the J apanese vowels /i/, /u/, and /e/ and pulse waves in human capillary ve ssels are implied by the analysis with the method of surrogate data, w e cannot conclude that these data have definite fractal structures. (C ) 1997 John Wiley & Sons, Inc.