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Nonlinear dynamics in infant respiration

  • Michael Small (a1)
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Abstract
Copyright
COPYRIGHT: © Australian Mathematical Society 1999
Corresponding author
Current Address:, Department of Physics, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, United Kingdom, e-mail: M.A.Small@hw.ac.uk
References
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[1]Abarbanel, H.D.I., Analysis of observed chaotic data, Institute for nonlinear science (Springer-Verlag, Berlin, Heidelberg, New York, 1996).
[2]Judd, K., ‘An improved estimator of dimension and some comments on providing confidence intervals’, Phys. D. 56 (1992), 216–228.
[3]Judd, K., ‘Estimating dimension from small samples’, Phys. D. 71 (1994), 421–429.
[4]Judd, K. and Mees, A., ‘On selecting models for nonlinear time series’, Phys. D. 82 (1995), 426–444.
[5]Judd, K. and Mees, A., ‘Embedding as a modelling problem’, Phys. D. 120 (1998), 273–286.
[6]Kantz, H. and Schreiber, T., Nonlinear time series analysis, Cambridge Nonlinear Science Series 7 (Cambridge University Press, Cambridge, 1997).
[7]Kaplan, D. and Glass, L., Understanding nonlinear dynamics, Texts in Applied Mathematics 19 (Springer-Verlag, Berlin, Heidelberg, New York, 1996).
[8]Small, M. and Judd, K., ‘Using surrogate data to test for nonlinearity in experimental data’, in International Symposium on Nonlinear Theory and its Applications 2 (Research Society of Nonlinear Theory and its Applications, IEICE, 1997), pp. 1133–1136.
[9]Small, M. and Judd, K., ‘Comparison of new nonlinear modelling techniques with applications to infant respiration’, Phys. D. 117 (1998), 283–298.
[10]Small, M. and Judd, K., ‘Detecting nonlinearity in experimental data’, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 8 (1998), 1231–1244.
[11]Small, M. and Judd, K., ‘Pivotal statistics for non-constrained realizations of composite null hypotheses in surrogate data analysis’, Phys. D. 120 (1998), 386–400.
[12]Small, M. and Judd, K.. ‘Detecting periodicity in experimental data using linear modeling techniques’, Phys. Rev. E. 59 (1999), 1379–1385.
[13]Small, M., Judd, K., Lowe, M. and Stick, S., ‘Is breathing in infants chaotic? Dimension estimates for respiratory patterns during quiet sleep’, J. Appl. Physiol. 86 (1999), 359–376.
[14]Small, M., Judd, K. and Mees, A., ‘Testing time series for nonlinearity’, Statistics and Computing (1999) (to appear).
[15]Small, M., Judd, K. and Stick, S., ‘Linear modelling techniques detect periodic respiratory behaviour in infants during regular breathing in quiet sleep’, (abstract), Am. J. Resp. Crit. Care. Med. 153 (1996), A79.
[16]Tokens, F., ‘Detecting nonlinearities in stationary time series’, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 3 (1993), 241–256.
[17]Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. and Farmer, J.D., ‘Testing for nonlinearity in time series: The method of surrogate data’, Phys. D. 58 (1992), 77–94.
[18]Theiler, J. and Prichard, D., ‘Constrained-realization Monte-Carlo method for hypothesis testing’, Phys. D. 94 (1996), 221–235.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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