Doublet-split-scaling of correlation integrals in non-linear dynamics and in neurobiology

摘要

The search for the low-dimensional attractor behaviour and the dynamic self-organization of neuronal systems, from an analysis of electroencephalographic (EEG) signals, must be carried out under conditions in which the signals are not stationary for more than a few seconds. We employ a technique that we have introduced for analyzing short signals obeying a differential equation and develop it further. The technique uses the fact that in plots of “slope curves” of d logC(r)/d logragainst logC(r),C(r)=correlation integral, for short time sequences, the dynamics may be “trans-embedding-scaled”, i.e. a horizontal power-law structure builds up, that is constructed from different slope curves (different embeddings), and appears at the right value of the correlation dimension, although no single slope curve exhibits