TIME REPARAMETRIZATION OF PHASE TRAJECTORIES AS A TEST FOR ATTRACTOR-RULED DYNAMICS - APPLICATION TO ELECTROENCEPHALOGRAPHIC ALPHA-WAVES

摘要

Time reparametrization of phase trajectories, which leaves their topological properties intact, is used to devise a means of checking the existence of an attractor. The test is applied in particular to electro-encephalographic signals, for which attractor behaviour is identified through observation of trans-embedding-scaled structures in families of slope curves of d log C(r)/d log r against log C(r), C(r) = correlation integral. The reparametrization test is quite sensitive to the artifactual attractor appearance occurring when an attention process transiently desynchronizes an alpha-wave, as occurs when interfering with a state of relaxed wakefulness in a subject having his eyes closed. An example is given of a trans-embedding-scaled structure obeying the previously required conditions, in particular the robustness conditions, which is found invariant against reparametrization. This finding supports under the specified conditions the use of trans-embedding-scaled structures in characterizing attractors. [References: 21]