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Slight parameter changes detection in biological models: a multiresolution approach. (English) Zbl 1021.92001
Summary: This paper deals with the automatic detection of slight parameter changes from the analysis of signals generated by nonlinear biological systems. The interest is focused here on investigating particular aspects of the relation between signal analysis and systems dynamics, involving the automatic detection of changes in parameters of nonlinear systems. The continuous multiresolution entropies combine advantages stemming from both entropy (Shannon and parametric \(q\)-entropy) and wavelet analysis, and have been shown to be sensitive to dynamical complexity changes. Classical statistical approaches offer a new tool that enables the automatic detection of such changes.
In this paper, multiresolution and standard tools for the automatic detection of slight parameter changes in nonlinear dynamical systems from the analysis of the corresponding time series are introduced and compared. The relevance of the multiresolution approach, together with its robustness in the presence of moderate noise, and its comparison is discussed in numerical simulations and applied to biological signals.

MSC:
92B05 General biology and biomathematics
37N25 Dynamical systems in biology
37M10 Time series analysis of dynamical systems
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[1] J. Bélair, L. Glass, U. an der Heiden, J. Milton, Dynamical disease, Mathematical analysis of human illness. American Institute of Physics, New York, 1995, pp. 1-7.
[2] Longtin, A., Chaos, 5, 209, (1995)
[3] Oseledec, V., Tr. mosk. mat. obsc., 19, 179, (1968)
[4] Eckmann, J.; Ruelle, D., Rev. mod. phys., 57, 617, (1985)
[5] Abarbanel, H.; Brown, R.; Sidorowich, J.; Tsimring, L., Rev. mod. phys., 65, 1331, (1993)
[6] Grassberger, P.; Schreiber, T.; Schaffrath, C., Int. J. bifurc. chaos, 1, 521, (1995)
[7] Pesin, Y., Russ. math. surv., 32, 55, (1977)
[8] M. Torres, L. Gamero, E. D’Attellis, in: I. Pitas (Ed.), 1995 IEEE Workshop on Non linear Signal and Image Processing (NSIP’95), Vol. II, IEEE, Thesaloniki, Greece, 1995, pp. 791-794.
[9] M.E. Torres, L. Gamero, P. Flandrin, P. Abry, in: A.F.L. Akram Aldroubi, M. Unser (Eds.), SPIE’97 Wavelet Applications in Signal and Image Processing V, Vol. 3169, SPIE International Society for Optical Engineering, Washington, 1997, pp. 400-407.
[10] Torres, M.E.; Gamero, L.G., Physica A, 286, 457, (2000)
[11] Havrda, J.; Charvat, F., Kybernetica, 3, 30, (1967)
[12] Darovczy, Z., Inf. control, 16, 36, (1970)
[13] Tsallis, C., Chaos, solitons fractals, 6, 539, (1995), and references therein
[14] Gamero, L.G.; Plastino, A.; Torres, M.E., Physica A, 246, 487, (1997)
[15] Y. Meyer, in: Hermann (Ed.), Ondelettes, Paris, France, 1990. · Zbl 0694.41037
[16] Meyer, Y., Wavelets, algorithms and applications, (1993), SIAM Philadelphia, USA
[17] M.E. Torres, Ph.D. thesis, Universidad Nacional de Rosario, Argentine, 1999 (Math.D.Thesis).
[18] Torres, M.E.; Añino, M.M.; Gamero, L.G.; Gemignani, M.A., Int. J. bifurc. chaos, 11, 967, (2001)
[19] Shannon, C., Bell syst. tech. J., 27, 379, (1948)
[20] Shensa, M., IEEE trans. signal process., 40, 2464, (1992)
[21] Rioul, O.; Duhamel, P., IEEE trans. inf. theory, 38, 569, (1992)
[22] P. Abry, Ondelettes et Turbulences, Multirésolutions, algorithmes de décomposition, invariance d’échelle et signaux de pression, Diderot Multimedia, France, 1997. · Zbl 0917.65115
[23] Akay, M., Deteccion and estimacion methods for biomedical signals, (1996), Academic Press San Diego, CA
[24] C. Matlab, Using Matlab Version 5, chapter 6, Data Analysis and Statistics, The Math Works, Inc., 1998, Natick, MA.
[25] Basseville, M.; Nikiforov, I., Detection of abrupt changes: theory and applications, (1993), Prentice-Hall Englewood Cliffs, NJ · Zbl 1407.62012
[26] Daubechies, I., Ten lectures on wavelets, (1992), SIAM Philadelphia, USA · Zbl 0776.42018
[27] Mallat, S.G., A wavelet tour of signal processing, (1999), Academic Press Cambridge · Zbl 0998.94510
[28] Friedrich, R.; Uhl, C., Evolution of dynamical structures in complex systems, (1992), Springer Berlin
[29] Moon, F.C., Chaotic and fractal dynamics, an introduction for applied scientists and engineers, (1992), Wiley New York
[30] Kelso, J.A.S.; Fuchs, A., Dynamical disease, mathematical analysis of human illness, (), 64-69
[31] Coullet, P.; Tresser, C.; Arnéodo, A., Phys. lett. A, 72, 268, (1979)
[32] F.H.L. da Silva, S. van Leeuwen, A. Rémond, Handbook of Electroencephalography and Clinical Neurophysiology, Vol. II: Clinical Application of Computer Analysis of EEG and other Neurophysiological Signals, Elsevier, Amsterdam, 1986.
[33] Fell, J.; Röschke, J.; Mann, K.; Schäffner, C., Electroencephalogr. clin. neurophysiol., 98, 401, (1996)
[34] Theiler, J.; Rapp, P.E., Electroencephalogr. clin. neurophysiol., 98, 213, (1996)
[35] Stam, C.; van Woerkom, T.; Pritchard, W.S., Electroencephalogr. clin. neurophysiol., 99, 214, (1996)
[36] Pijn, J.P.; van Neerven, J.; Noest, A.; Lopes da Silva, F.F.H., Electroencephalogr. clin. neurophysiol., 79, 371, (1991)
[37] Anokhin, A.P., Electroencephalogr. clin. neurophysiol., 99, 63, (1996)
[38] Rombouts, S.; Keunen, R.; Stam, C., Phys. lett. A, 202, 352, (1995)
[39] Pritchard, W.S.; Duke, D.W.; Krieble, K.K., Psychophysiology, 32, 486, (1995)
[40] Kopitzki, K.; Warnke, P.; Timmer, J., Phys. rev. E, 58, 4849, (1998)
[41] Gotman, J., ()
[42] Babloyantz, A., (), 241-245
[43] Basar, E., Chaos in brain function, (1990), Springer Berlin
[44] G. Meyer-Kress, S. Layne, in: M.F.S.S.H. Koslow, A.J. Mandel (Eds.), Perspectives in Biological Dynamics and Theoretical Medicine, Annals New York Academy Science, New York, USA, 1987, No. 504.
[45] L. Iasemidis, J.C. Sackellares, H. Zaveri, W. Williams, 25th Annual Rocky Mountain Bioing, Symposium, Colorado Springs, CO, USA, Vol. 1201, 1988.
[46] Iasemidis, L.; Sackellares, J.; Zaveri, H.; Williams, W., Brain topogr., 2, 187, (1990)
[47] Papoullis, A., Probability, random variables and stochastic processes, electrical and electronic engineering series, (1991), McGraw-Hill Singapore
[48] Torres, M.; Gamero, L.; D’Attellis, E., Latin am. appl. res., 53, 53, (1995)
[49] D’Attellis, C., Wavelet theory and harmonic analysis in applied sciences, (), 227-262
[50] A. Capurro, et al., Technical Report No. 3184. INRIA-Rapport de recherche, endc. Analyt 21105, ISSN 0249-6399.
[51] Capurro, A., Physica A, 257, 149, (1998)
[52] Page, E., Biometrika, 41, 100, (1954)
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