Nonlinear data analysis of experimental (EEG) data and comparison with theoretical (ANN) data

Complexity

Volumn 7, Issue 3, 2002, Pages 30-40

  Das, Atin ^a   Das, Pritha ^a   Roy, A B ^a  

^a JADAVPUR UNIVERSITY   (India)

Author keywords

Fractal and correlation dimension; Lyapunov exponents; Nonlinearity; Surrogate data

Indexed keywords

EID: 84995572285     PISSN: 10762787     EISSN: 10990526     Source Type: Journal    
DOI: 10.1002/cplx.10024     Document Type: Article

References (39)

1. Knyazeva, M.G.; Kiper, D.C.; Vildavski, V.Y.; Despland, P.A.; Maeder-Ingvar, M.; Innocent, G.M. Visual stimulus-dependent changes in interhemispheric EEG coherence in humans. J Neurophysiol 1999, 82, 3095–3107.
2. Mayer-Kress, G. Complexity of EEG signals during exposure to synthesized music. Integrative Physiol Behav Sci 1998, 33, 92–93.
3. Birbaumer, N.; Lutzenberger, W.; Rau, H.; Mayer-Kress, G.; Braun, C. Perception of music and dimensional complexity of brain activity. Int J Bifurcations Chaos 1996, 6, 267–278.
4. Lutzenberger, W.; Preissl, H.; Pulvermüller, F. Fractal dimension of EEG time series and underlying brain processes. Biol Cybernet 1995, 73, 477–482.
5. Mölle, M.; Marshall, L.; Lutzenberger, W.; Pietrowsky, R.; Fehm, H.L.; Born, J. Enhanced dynamic complexity in the human EEG during creative thinking. Neurosci Lett 1996, 208, 61–64.
6. Rapp, P.E.; Bashore, T.; Martinerie, J.; Albano, A.; Zimmerman, I.; Mess, A. Dynamics of brain electrical activity. Brain Topography 1989, 2, 99–118.
7. Wright, J. Method for calculating a Lyapunov exponent. Phys Rev A 1984, 29, 2924–2928.
8. Wright, J.J.; Liley, D.T.J. Dynamics of the brain at global and microscopic scales. Neural Netw EEG Behav Brain Sci 1996, 19, 285–320.
9. Wright, J.J. Personal communication, 2001.
10. Casdagli, M.C.; Iasemidis, L.D.; Savit, R.S.; Glimore, R.L.; Roper, S.N.; Sacklelares, J.C. Non-linearity in invasive EEG recordings from patients with temporal lobe epilepsy. Eletroencephalogr Clin Neurophysiol 1997, 98, 1102.
11. Babloyantz, A. Chaotic dynamics in brain activity. In: Dynamics of Sensory and Cognitive Processing by the Brain; Basar, E., Ed.; Springer: Berlin, 1988; p 38.
12. Palus, M. Nonlinearity in normal human EEG: Cycles, temporal asymmetry, nonstationarity and randomness, not chaos. Biol Cybernet 1996, 75, 389–396.
13. Palus, M. Chaotic measures and real-world systems. In: Nonlinear Analysis of Physiological Data; Kantz, H.; Kurths, J.; Mayer-Kress, G., Eds.; Springer: Berlin, 1998; p 49.
14. Palus, M. Nonlinear dynamics in the EEG analysis. Disappointments and perspectives. In: Nonlinear Dynamics and Brain Functioning; Pradhan, N.; Rapp, P.E.; Sreenivasan, R., Eds.; Novascience: New York, 1999.
15. Palus, M. Personal communication, 2001.
16. Theiler, J. Don't bleach chaotic data. Chaos 1993, 3, 771–782.
17. Pritchard, W.S.; Duke, D.W.; Krieble, K.K. Dimensional analysis of human EEG II: Surrogate data testing indicates non-linearity but not low-dimensional chaos. Psychophysiology 1995, 32, 486–491.
18. Babloyantz, A.; Destexhe, A. Low dimensional chaos in an instance of epilepsy. Proc Natl Acad Sci USA 1986, 83, 3513–3517.
19. Freeman, W.J.; Yao, Y.; Burke, B. Central pattern generating and recognizing in olfactory bulb: A correlation learning rule. Neural Netw 1988, 1, 277–288.
20. Schreiber, T. Interdisciplinary application of nonlinear time series methods. Phys Rep 1999, 308, 2.
21. Mayer-Kress, G.; Layne, S.P. Dimensionality of the human eltroencephelogram. Ann NY Acad Sci 1987, 504, 62–86.
22. Mayer-Kress, G. Personal communication, 2001.
23. Theiler, J.; Eubank, S.; Longtin, A.; Galdrikian, B.; Farmer, J. Testing for nonlinearity in time series: The method of surrogated data. Physica D 1992, 58, 77–94.
24. Watters, P.A. Fractal structure in the encephelogram. Complexity Int 1998, 5.
25. Grassberger, P.; Procaccia, I. Measuring the strangeness of strange attractos. Physica D 1983, 9, 189–208.
26. Schreiber, T. Constrained randomization of time series data. Phys Rev Lett 1998, 80, 2105.
27. Stam, C.; Pijn, J.; Suffczynski, P.; da Silva, L. Dynamics of the alpha rhythm: Evidence for non-linearity? Clin Neurophysiol 1999, 110, 1801–1813.
28. Jeong, J.; Jeong-Ho, C.; Soo Yong, K.; Seol-Heui, H. Nonlinear dynamic analysis of the EEG in patients with Alzheimer's disease and vascular dementia. J Clin Neurophysiol 2001, 18, 58–67.
29. Das, A.; Das, P.; Roy, A.B. Chaos in three dimensional neural network. Appl Math Model 2000, 24, 511–522.
30. Hegger, R.; Kantz, H.; Schreiber, T. Practical implementation of nonlinear time series methods: The TISEAN package. CHAOS 1999, 9, 413–435.
31. Das, A.; Das, P.; Roy, A.B. Chaos in three dimensional neural network. Int J Bifurcation Chaos 2001, Forthcoming.
32. Kennel, M.B.; Brown, R.; Abarbanel, H.D.I. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 1992, 45, 3403–3411.
33. Liebert, W.; Pawelzik, K.; Schuster, H.G. Optimal embeddings of chaotic attractors from topological considerations. Europhys Lett 1991, 14, 521–526.
34. Schreiber, T. Is nonlinearity evident in time series of brain electrical activity. Proceedings: Chaos in Brain; Lehnertz, K.; Elger, C.E.; Amhold, J.; Grassberger, P., Eds.; World Science: Singapore, 2000.
35. Sabin, G.C.W.; Summers, D. Chaos in a periodically forced predator-prey ecosystem model. Math Biosci 1993, 113, 91–113.
36. Skinner, J.E.; Pratt, C.M.; Vybiral, T. A reduction in the correlation dimension of heartbeat intervals precedes imminent ventricular fibrillation in human subjects. Am Heart J 3, 1993, 125, 731–743.
37. Wolf, A.; Swift, J.B.; Swinney, L.H.; Vastano, J.A. Determining Lyapunov exponent from a time series. Physica D 1985, 16, 285–317.
38. Peitgen, H.O.; Jurgens, H.; Sanpe, D. Lyapunov exponents and chaotic attractors. Chaos and Fractals—New Frontiers of Science. Springer: New York, 1992; pp 719–720.
39. Rosenstein, M.T.; Collins, J.J.; De Luca, C.J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 1993, 65, 117–120.