Fractal dimensions of short EEG time series in humans

Neuroscience Letters

Volumn 225, Issue 2, 1997, Pages 77-80

  Preißl, Hubert ^a   Lutzenberger, Werner ^a   Pulvermüller, Friedemann ^a   Birbaumer, Niels ^a,b  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

Chaos; Dimension; Electroencephalogram; Non linearity; Surrogate data

Indexed keywords

ARTICLE; CONTROLLED STUDY; DATA ANALYSIS; ELECTROENCEPHALOGRAM; HUMAN; HUMAN EXPERIMENT; NORMAL HUMAN; PRIORITY JOURNAL;

ELECTROENCEPHALOGRAPHY; FRACTALS; HUMANS; TIME FACTORS;

EID: 0031552375     PISSN: 03043940     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3940(97)00192-4     Document Type: Article

References (21)

1. Achermann P., Hartmann R., Gunzinger A., Guggenbühl W., Borbely A.A. All-night sleep EEG and artificial stochastic control signals have similar correlation dimensions. Electroenceph. clin. Neurophysiol. 90:1994;384-387.
2. Berge, P., Pomeau, Y. and Vidal, C., Order Within Chaos, Wiley, New York, 1986, 329 pp.
3. Broomhead D.S., King G.P. Extracting qualitative dynamics from experimental data. Physica D. 20:1986;217-236.
4. Eckmann J.-P., Ruelle D. Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems. Physica D. 56:1992;185-187.
5. Elbert T., Ray W.J., Kowalik Z.J., Skinner J.E., Graf K.E., Birbaumer N. Chaos and physiology: deterministic chaos in excitable cell assemblies. Phys. Rev. 74:1994;1-47.
6. Elbert T., Rockstroh B. Threshold regulation - a key to the understanding of the combined dynamics of EEG and event related potentials. J. Psychophysiol. 4:1987;317-333.
7. Kim Y.M., Krieble K.K., Kim C.M., Reed J., Rae-Grant A.D. Differentiation of alpha coma from awake alpha by nonlinear dynamics of electroencephalography. Electroenceph. clin. Neurophysiol. 98:1995;35-41.
8. Lutzenberger W., Elbert T., Birbaumer N., Ray W.J., Schupp H.T. The scalp distribution of fractal dimension of the EEG and its variation with mental task. Brain Topogr. 5:1992;27-34.
9. Lutzenberger W., Preißl H., Pulvermüller F. Fractal dimension of electroencephalographic time series and underlying brain processes. Biol. Cybern. 73:1995;477-482.
10. Osborne A.R., Provenzale A. Finite correlation dimension for stochastic systems with power-law spectra. Physica D. 35:1989;357-381.
11. Packard N.H., Crutchfield J.P., Farmer J.D., Shaw R.S. Geometry from a time series. Phys. Rev. Lett. 45:1980;712-716.
12. Palm G. Comments on the paper `Threshold regulation - a key to the understanding of the combined dynamics of EEG and event-related potentials' by T. Elbert and B. Rockstroh, J. Psychophysiol. 4:1987;335-337.
13. Preißl, H. and Aertsen, A.M.H.J., Reconstruction and characterisation of neuronal dynamics: how attractive is chaos? In A. Aertsen and V. Braitenberg (Eds.), Information Processing in the Cortex: Experiments and Theory, Springer-Verlag, Berlin, 1992, pp. 285-297.
14. Procaccia I. Complex or just complicated. Nature. 333:1988;489-499.
15. Röschke J., Aldenhoff J. The dimensionality of human's electroencephalogram during sleep. Biol. Cybern. 64:1991;307-313.
16. Röschke J., Aldenhoff J.B. A nonlinear approach to brain function: deterministic chaos and sleep EEG. Sleep. 15:1992;95-101.
17. Skarda C.A., Freeman W.J. How brains make chaos in order to make sense of the world. Behav. Brain Sci. 10:1987;161-195.
18. Skinner J.E., Molnar M., Tomberg C. The point correlation dimension: performance with nonstationary surrogate data and noise. Integr. Physiol. Behav. Sci. 29:1994;217-234.
19. Smith L.A. Intrinsic limits on dimension calculation. Phys. Lett. A. 133:1988;283-288.
20. Theiler J. Spurious dimensions from correlation algorithms applied to limited time series data. Phys. Rev. A. 34:1986;2427-2432.
21. Theiler J., Eubank S., Longtin A., Galdrikian B., Farmer J. Testing for nonlinearity in time series: the method of surrogate data. Physica D. 58:1992;77-94.