Abstract
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 α-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.
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Hénoune, M.O., Cerf, R. Time reparametrization of phase trajectories as a test for attractor-ruled dynamics: application to electroencephalographic α-waves. Biol. Cybern. 73, 235–243 (1995). https://doi.org/10.1007/BF00201425
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DOI: https://doi.org/10.1007/BF00201425