Forcing Function Effects on Nonlinear Trajectories: Identifying Very Local Brain Dynamics

Nonlinear Dynamics, Psychology, and Life Sciences - Tập 7 - Trang 139-159 - 2003
Robert A. M. Gregson1, Kerry Leahan1
1Australian National University, Canberra Australia

Tóm tắt

Effects of imposing a sinusoidal acoustic and visual forcing function at various frequencies onto an EEG process are examined in terms of various indices of the nonlinear dynamics. Conjoint use of four methods of data analysis; Lyapunov exponents, the entropic analogue of the Schwarzian derivative, surrogate distributions, and higher-order kernel analyses in the time domain, is illustrated. Local epochs with unstable dynamics are identifed on very short series.

Tài liệu tham khảo

Aoki, M. (1987). State-space modeling of time series. Berlin: Springer-Verlag. Argoul, P. & Arneodo, A. (1986). Lyapunov exponents and phase transitions. In L. Arnold, & V. Wihstutz (Eds.), Lyapunov exponents. Lecture Notes in Mathematics No. 1186 (pp. 338–360). Berlin: Springer-Verlag. Baars, B. J. (2001). The brain basis of a “consciousness monitor”: Scientific and medical significance. Consciousness and Cognition, 10, 159–164. Baccalá, L. A. & Sameshima, K. (2001). Partial directed coherence: A new concept in neural structure determination. Biological Cybernetics, 84, 463–474. Bowman, A. W. (1980). A note on consistency of the kernel method for the analysis of categorical data. Biometrika, 67, 682–684. Boys, R. J., Henderson, D. A. & Wilkinson, D. J. (2000). Detecting homogeneous segments in DNA sequences by using hidden Markov models. Applied Statistics, 49, 269–285. Bruhn, J., Röpcke, H., Rehberg, B., Bouillion, T., & Hoeft, A. (2000). Electroencephalogram approximate entropy correctly classifies the occcurrence of burst suppression pattern as increasing anesthetic drug effect. Anesthesiology, 93, 981–985. Contopoulos, G. (1998). Dynamical spectra and the onset of chaos. In J. R. Buchler, S. T. Gottesman, & H. E. Kandrup (Eds.), Nonlinear dynamics and chaos: A festschrift in honor of George Contopoulos (pp. 14–40). New York: New York Academy of Sciences. Fujisaka, H. (1983). Statistical dynamics generated by fluctuations of local Lyapunov exponents. Progress in Theoretical Physics, 70, 1264–1275. Geake, J. G. & Gregson, R. A. M. (1999). Modelling the internal generation of rhythm as an extension of nonlinear psychophysics. Musicae Scientiae, 3, 217–236. Glass, P.S., Bloom, M., Kearse, L., Rosow, C., Sebel, P. & Mauberg, P. (1997). Bispectral analysis measures sedation and memory effects of propofol, midazolam, isoflurane, and alfentanil in healthy volunteers. Anesthesiology, 86, 836–847. Gregson, R. A. M. (1988). Nonlinear psychophysical dynamics. Hillsdale, NJ: Lawrence Erlbaum Associates. Gregson, R. A. M. (2000). Elementary identification of nonlinear trajectory entropies. Australian Journal of Psychology, 52, 94–99. Gregson, R. A. M. (2001a). Scaling quasi-Periodic psychophysical functions. Behaviormetrika, 29, 41–57. Gregson, R. A. M. (2001b). Nonlinearity, nonstationarity, and concatenation: The characterisation of brief time series. Proceedings of the 10th Australian Mathematical Psychology Conference. Newcastle, NSW. December, 2001 Grießbach, G. (1999). Methods of time-variant bispectral analysis for the investigation of transient quadratic phase couplings in biomedical signals. (www-stja.tu-ilmenau.de/e_forschung/4_bispektralanalyse.html) Grießbach, G. & Witte, H. (1997). Complex adaptive procedures for EEG monitoring. In H. Witte, U. Zwiener, B. Schack, & A. Doering (Eds.), Quantitative and topological EEG and MEG analysis (pp. 237–248). Erlangen: Druckhaus Mayer. Heath, R. A. (2000). Nonlinear dynamics: techniques and applications in psychology. Mahwah, NJ: Lawrence Erlbaum Associates. Hinich, M. J. Testing for gaussianity and linearity of a stationary time series. Journal of Time Series Analysis, 3, 169–176. Kapitaniak, T. (1990). Chaos in systems with noise (2nd Edn) Singapore: World Scientific. Kearse, L. A., Manberg, P., Chamoun, N., deBros, F. & Zaslavsky, A. (1994). Bispectral analysis of the electroencephalogram correlates with patient movement to skin incision during propofol/nitrous oxide anesthesia. Anesthesiology, 81, 1365–1370. Kearse, L. A., Rosow, C., Zaslavsky, A., Connors, P., Dershwitz, M. & Denman, V. (1998). Bispectral analysis of the electroecephalogram predicts conscious processing of information during propofol sedation and hypnosis. Anesthesiology, 88, 25–34. Kedem, B. (1994). Time series analysis by higher-order crossings. New York: IEEE Press. Kopell, N. & Ermentrout, G. B. (1990). Phase transitions and other phenomena in chains of coupled oscillators. SIAM Journal of Applied Mathematics, 50, 1014–1052. Levi, S. (1981). Qualitative analysis of the periodically forced relaxation oscillator. Memoirs of the American Mathematical Association, 32. New York: American Mathematical Association. Mandelbrot, B. B. (1990). Fractal geometry, what is it, and what does it do? In Fleischmann, M., Tildesley, D. J. & Ball, R. C. (Eds) Fractals in the Natural Sciences (pp. 3–16). Princeton, NJ: Princeton University Press. Marmarelis, P. Z. & Marmarelis, V. Z. (1978). Analysis of physiological systems. New York: Plenum Press. McLaughlin, S., Stogioglou, A. & Fackrell, J. (1995). Introducing higher order statistics (HOS) for the detection of nonlinearities. from: UK Nonlinear News. [www.amsta.leeds. ac.uk/Applied/news.dir] Miyano, H. (2001). Identification model based on the maximum information entropy principle. Journal of Mathematical Psychology, 45, 27–42. Nunez, P. L. (1995). Neocortical dynamics and human EEG rhythms. New York: Oxford University Press. Petzold, P. & Haubensak, G. (2001). Higher order sequential effects in psychophysical judgments. Perception and Psychophysics, 63, 969–978. Proakis, J. G., Rader, C. M., Ling, F. & Nikias, C. L. (1992). Advanced digital signal processing. New York: Macmillan. Rampil, I.J. (1998). A primer for EEG signal processing in anesthesia. Anesthesiology, 89, 980–1002. Schreiber, T. (1997). Detecting and analysing nonstationarity in a time series with nonlinear cross-predictions. Physics Review Letters, 78, 843–847. Schwarz, H. A. (1868). Über einige Abbildungs aufgaben. Journal für reine und angewandte Mathematik (Crelle), 70, 105–120. Singher, D. (1978). Stable Orbits and Bifurcation of Maps of the Interval. SIAM Journal of Applied Mathematics, 35(2), 260–267. Sugihara, G. & May, R. M. (1990). Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature, 344, 734–741. Theiler, J., Galdrikian, B., Longtin, A., Eubank, S. & Farmer, J. (1992). Testing for nonlinearity in time series: The method of surrogate data. Physica D, 58, 77–94. Thomasson, N., Hoeppner, T. J., Webber, C. L. Jr. & Zbilut, J. P. (2001). Recurrence quantification in epileptic EEGs. Physics Letters A, 279, 94–101. Wiggins, S. (1992). Chaotic transport in dynamical systems. New York: Springer-Verlag. Witte, H., Schelenz, Ch., Specht, M., Jäger, H., Putsche, P., Arnold, M., Leistritz, & Reinhart, K. (1999). Interrelations between EEG frequency components in sedated intensive care patients during burst-suppression period. Neurosciences Letters, 277, 311–314.