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Volumn 2, Issue , 2000, Pages 1-39

Nonlinear dynamics time series analysis

Author keywords

Chaos; Equations; Mathematical model; Noise; Nonlinear dynamical systems; Oscillators; Time series analysis

Indexed keywords

CHAOS THEORY; DYNAMICAL SYSTEMS; HARMONIC ANALYSIS; MATHEMATICAL MODELS; NONLINEAR DYNAMICAL SYSTEMS; NONLINEAR EQUATIONS; OSCILLATORS (ELECTRONIC);

EID: 84975828536     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1109/9780470545379.ch1     Document Type: Chapter
Times cited : (77)

References (50)
  • 1
    • 0002392160 scopus 로고
    • A personal overview of non-linear time series analysis from a chaos perspective
    • H. Tong, A personal overview of non-linear time series analysis from a chaos perspective. Scand. J. Stat. 22: 399-445, 1995.
    • (1995) Scand. J. Stat. , vol.22 , pp. 399-445
    • Tong, H.1
  • 2
    • 0342426385 scopus 로고
    • A dynamical systems approach to time series analysis
    • T. Mullin, (ed.), Chap. 2. Oxford: Oxford University Press
    • T. Mullin, A dynamical systems approach to time series analysis. In The Nature ofChaos, T. Mullin, (ed.), Chap. 2. Oxford: Oxford University Press, 1993.
    • (1993) The Nature ofChaos
    • Mullin, T.1
  • 3
    • 0001974770 scopus 로고
    • Statistical aspects of chaos: A review
    • O. E. Barndorff-Nielsen, J. L. Jensen, and W. S. Kendall, (eds.), Chap. 3. London: Chapman & Hall
    • V. Isham, Statistical aspects of chaos: a review. In Networks and Chaos-Statistical and Probabilistic Aspects, O. E. Barndorff-Nielsen, J. L. Jensen, and W. S. Kendall, (eds.), Chap. 3. London: Chapman & Hall, 1993.
    • (1993) Networks and Chaos-Statistical and Probabilistic Aspects
    • Isham, V.1
  • 4
    • 0000202504 scopus 로고
    • Chaos and deterministic versus stochastic non-linear modelling
    • M. Casdagli, Chaos and deterministic versus stochastic non-linear modelling. J. R. Stat. Soc. B. 54: 303-328, 1992.
    • (1992) J. R. Stat. Soc. B. , vol.54 , pp. 303-328
    • Casdagli, M.1
  • 5
    • 0000121132 scopus 로고
    • An experimentalist’s introduction to the observation of dynamical systems
    • Hao Bai-Lin, (ed.), Singapore: World Scientific
    • N. Gershenfeld, An experimentalist’s introduction to the observation of dynamical systems. In Directions in Chaos, Vol. 2, Hao Bai-Lin, (ed.), pp. 310-383. Singapore: World Scientific, 1988.
    • (1988) Directions in Chaos , vol.2 , pp. 310-383
    • Gershenfeld, N.1
  • 6
    • 0019815049 scopus 로고
    • Phase locking, period doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells
    • M. R. Guevara, L. Glass, and A. Shrier, Phase locking, period doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Science 214: 1350-1352, 1981.
    • (1981) Science , vol.214 , pp. 1350-1352
    • Guevara, M.R.1    Glass, L.2    Shrier, A.3
  • 7
    • 0025105082 scopus 로고
    • Supernormal excitability as a mechanism of chaotic dynamics of activation in cardiac Purkinje fibers
    • D. R. Chialvo, D. C. Michaels, and J. Jalife, Supernormal excitability as a mechanism of chaotic dynamics of activation in cardiac Purkinje fibers. Circ. Res. 66: 525-545, 1990.
    • (1990) Circ. Res. , vol.66 , pp. 525-545
    • Chialvo, D.R.1    Michaels, D.C.2    Jalife, J.3
  • 9
    • 0026758237 scopus 로고
    • Forced oscillations in sympathetic nerve discharge
    • Z. S. Huang, G. L. Gebber, S. Zhong, and S. Barman, Forced oscillations in sympathetic nerve discharge. Am. J. Physiol. 263: R564-R571, 1992.
    • (1992) Am. J. Physiol. , vol.263 , pp. R564-R571
    • Huang, Z.S.1    Gebber, G.L.2    Zhong, S.3    Barman, S.4
  • 10
    • 0026050335 scopus 로고
    • Chaos in blood flow control in genetic and renovascular hypertensive rats
    • K. P. Yip, N. H. Holstein-Rathlou, and D. J. Marsh, Chaos in blood flow control in genetic and renovascular hypertensive rats. Am. J. Physiol. 261: F400-F408, 1991.
    • (1991) Am. J. Physiol. , vol.261 , pp. F400-F408
    • Yip, K.P.1    Holstein-Rathlou, N.H.2    Marsh, D.J.3
  • 11
    • 0028841436 scopus 로고    scopus 로고
    • Complexity and “chaos” in blood pressure after baroreceptor denervation of conscious dogs
    • C. D. Wagner, R. Mrowka, B. Nafz, and P. B. Persson, Complexity and “chaos” in blood pressure after baroreceptor denervation of conscious dogs. Am. J. Physiol. 269: H1760-H1766, 1996.
    • (1996) Am. J. Physiol. , vol.269 , pp. H1760-H1766
    • Wagner, C.D.1    Mrowka, R.2    Nafz, B.3    Persson, P.B.4
  • 12
    • 84973949757 scopus 로고
    • How brains make chaos in order to make sense of the world
    • C. A. Skarda and W. J. Freeman, How brains make chaos in order to make sense of the world. Behav. Brain Sci. 10: 161-195, 1987.
    • (1987) Behav. Brain Sci. , vol.10 , pp. 161-195
    • Skarda, C.A.1    Freeman, W.J.2
  • 14
    • 0343970775 scopus 로고
    • Neimark bifurcation, almost periodicity and chaos in the forced van der Pol-Duffing system in the neighbourhood of the principal resonance
    • W. Szemplinska-Stupnicka and J. Rudowski, Neimark bifurcation, almost periodicity and chaos in the forced van der Pol-Duffing system in the neighbourhood of the principal resonance. Phys. Lett. A 192: 201-206, 1994.
    • (1994) Phys. Lett. A , vol.192 , pp. 201-206
    • Szemplinska-Stupnicka, W.1    Rudowski, J.2
  • 15
    • 84957234450 scopus 로고
    • How random is a coin toss?
    • J. Ford, How random is a coin toss? Phys. Today 36(4): 40, 1983.
    • (1983) Phys. Today , vol.36 , Issue.4 , pp. 40
    • Ford, J.1
  • 16
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem
    • V. I. Oseledec, A multiplicative ergodic theorem. Trans. Moscow. Math. Soc. 19: 197-231, 1968.
    • (1968) Trans. Moscow. Math. Soc. , vol.19 , pp. 197-231
    • Oseledec, V.I.1
  • 17
    • 35949037738 scopus 로고
    • Kolmogorov entropy and numerical experiments
    • G. Benettin, L. Galgani, and J. M. Strelcyn, Kolmogorov entropy and numerical experiments. Phys. Rev. A 14: 2338-2345, 1976.
    • (1976) Phys. Rev. A , vol.14 , pp. 2338-2345
    • Benettin, G.1    Galgani, L.2    Strelcyn, J.M.3
  • 18
    • 0021224909 scopus 로고
    • Determining Lyapunov exponents from a time series
    • A. Wolfe, J. B. Swift, H. L. Swinney, and J. A. Vastano, Determining Lyapunov exponents from a time series. Physica D 16: 285-317, 1985.
    • (1985) Physica D , vol.16 , pp. 285-317
    • Wolfe, A.1    Swift, J.B.2    Swinney, H.L.3    Vastano, J.A.4
  • 19
    • 0007287076 scopus 로고
    • Multiperiodic flows, chaos and Lyapunov exponents
    • H. Fujisaka, Multiperiodic flows, chaos and Lyapunov exponents. Prog. Theor. Phys. 68: 1105-1119, 1982.
    • (1982) Prog. Theor. Phys. , vol.68 , pp. 1105-1119
    • Fujisaka, H.1
  • 20
    • 0012841756 scopus 로고
    • Numerical computations on a stochastic parameter related to Kolmogorov entropy
    • M. Casartelli, E. Diana, L. Galgani, and A. Scotti, Numerical computations on a stochastic parameter related to Kolmogorov entropy. Phys. Rev. A 13: 1921-1925, 1976.
    • (1976) Phys. Rev. A , vol.13 , pp. 1921-1925
    • Casartelli, M.1    Diana, E.2    Galgani, L.3    Scotti, A.4
  • 21
    • 0000672504 scopus 로고
    • A numerical approach to ergodic problem of dissipative systems
    • I. Shimada and T. Nagashima, A numerical approach to ergodic problem of dissipative systems. Prog. Theor. Phys. 61: 1605-1613, 1979.
    • (1979) Prog. Theor. Phys. , vol.61 , pp. 1605-1613
    • Shimada, I.1    Nagashima, T.2
  • 22
    • 0018989294 scopus 로고
    • Lyapunov characteristic exponents for smooth dynamical systems: A method for computing all of them
    • G. Benettin, L. Galgani, A. Giorgilli, and J.-M. Strelcyn, Lyapunov characteristic exponents for smooth dynamical systems: A method for computing all of them. Meccanica 15: 9-19, 1980.
    • (1980) Meccanica , vol.15 , pp. 9-19
    • Benettin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.-M.4
  • 24
    • 0346372923 scopus 로고
    • The infinite number of generalized dimensions of fractals and strange attractors
    • H. G. E. Hentschel and I. Procaccia, The infinite number of generalized dimensions of fractals and strange attractors. Physica D 8: 435-444, 1983.
    • (1983) Physica D , vol.8 , pp. 435-444
    • Hentschel, H.G.E.1    Procaccia, I.2
  • 25
    • 0001640825 scopus 로고
    • Functional differential equations and the approximation of fixed points
    • Berlin: Springer-Verlag
    • J. Kaplan and J. Yorke, Functional differential equations and the approximation of fixed points. In Lecture Notes in Mathematics, No. 730. Berlin: Springer-Verlag, 1979.
    • (1979) Lecture Notes in Mathematics , Issue.730
    • Kaplan, J.1    Yorke, J.2
  • 26
    • 33646981873 scopus 로고
    • Characterization of strange attractors
    • P. Grassberger and I. Procaccia, Characterization of strange attractors. Phys. Rev. Lett. 50: 346-349, 1983.
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 346-349
    • Grassberger, P.1    Procaccia, I.2
  • 27
    • 0001285133 scopus 로고
    • Deterministic chaos: The science and the fiction
    • D. Ruelle, Deterministic chaos: The science and the fiction. Proc. R. Soc. Lond. A 427: 241-248, 1990.
    • (1990) Proc. R. Soc. Lond. A , vol.427 , pp. 241-248
    • Ruelle, D.1
  • 28
    • 0039097317 scopus 로고
    • Comments on “Deterministic chaos: The science and the fiction” by D. Ruelle
    • C. Essex and M. A. H. Nerenberg, Comments on “Deterministic chaos: the science and the fiction” by D. Ruelle. Proc. R. Soc. Lond. A 435: 287-292, 1991.
    • (1991) Proc. R. Soc. Lond. A , vol.435 , pp. 287-292
    • Essex, C.1    Nerenberg, M.A.H.2
  • 29
    • 0242328535 scopus 로고
    • An amendment to the fundamental limit on dimension calculations
    • S.-Z. Hong and S.-M. Hong, An amendment to the fundamental limit on dimension calculations. Fractals 2: 123-125, 1994.
    • (1994) Fractals , vol.2 , pp. 123-125
    • Hong, S.-Z.1    Hong, S.-M.2
  • 31
    • 0000779360 scopus 로고
    • Detecting strange attractors in turbulence
    • D. A. Rand and L. S. Young, eds. Berlin: Springer
    • F. Takens, Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence, D. A. Rand and L. S. Young, eds. Berlin: Springer, 1981.
    • (1981) Dynamical Systems and Turbulence
    • Takens, F.1
  • 32
    • 0000920052 scopus 로고
    • Rigorous verification of trajectories for computer simulation of dynamical systems
    • T. Sauer and J. A. Yorke, Rigorous verification of trajectories for computer simulation of dynamical systems. Nonlinearity 4: 961-979, 1991.
    • (1991) Nonlinearity , vol.4 , pp. 961-979
    • Sauer, T.1    Yorke, J.A.2
  • 34
    • 0025199496 scopus 로고
    • Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series
    • G. Sugihara and R. M. May, Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344: 734-741, 1990.
    • (1990) Nature , vol.344 , pp. 734-741
    • Sugihara, G.1    May, R.M.2
  • 35
    • 0037723718 scopus 로고
    • Distinguishing chaos from noise
    • Chap. 7. Oxford: Oxford University Press
    • D. Holton and R. M. May, Distinguishing chaos from noise. In The Nature of Chaos, Chap. 7. Oxford: Oxford University Press, 1993.
    • (1993) The Nature of Chaos
    • Holton, D.1    May, R.M.2
  • 36
    • 35949011725 scopus 로고
    • Singular-value decomposition and the Grassberger-Procaccia algorithm
    • A. M. Albano, J. Muench, C. Schwartz, A. I. Mees, and P. E. Rapp, Singular-value decomposition and the Grassberger-Procaccia algorithm. Phys. Rev. A 38: 3017, 1988.
    • (1988) Phys. Rev. A , vol.38 , pp. 3017
    • Albano, A.M.1    Muench, J.2    Schwartz, C.3    Mees, A.I.4    Rapp, P.E.5
  • 37
    • 0003145759 scopus 로고
    • Phase portraits from a time series: A singular system approach
    • G. P. King, R. Jones, and D. S. Broomhead, Phase portraits from a time series: A singular system approach. Nucl. Phys. B 2: 379, 1987.
    • (1987) Nucl. Phys. B , vol.2 , pp. 379
    • King, G.P.1    Jones, R.2    Broomhead, D.S.3
  • 38
    • 34548696055 scopus 로고
    • Independent coordinates for strange attractors from mutual information
    • A. M. Fraser and H. Swinney, Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33: 1134-1139, 1986.
    • (1986) Phys. Rev. A , vol.33 , pp. 1134-1139
    • Fraser, A.M.1    Swinney, H.2
  • 39
    • 30244464950 scopus 로고
    • Proper choice of the time delay for the analysis of chaotic time series
    • W. Liebert and H. G. Schuster, Proper choice of the time delay for the analysis of chaotic time series. Phys. Lett. A 142: 107, 1989.
    • (1989) Phys. Lett. A , vol.142 , pp. 107
    • Liebert, W.1    Schuster, H.G.2
  • 40
    • 0002064172 scopus 로고
    • Using higher-order correlations to define an embedding window
    • A. M. Albano, A. Passamante, and M. E. Farrell, Using higher-order correlations to define an embedding window. Physica D 54: 85, 1991.
    • (1991) Physica D , vol.54 , pp. 85
    • Albano, A.M.1    Passamante, A.2    Farrell, M.E.3
  • 41
    • 0001089951 scopus 로고
    • Mutual information, strange attractors, and the optimal estimation of dimension
    • J. M. Martinerie, A. M. Albano, A. I. Mees, and P. E. Rapp, Mutual information, strange attractors, and the optimal estimation of dimension. Phys. Rev. A. 45: 7058, 1992.
    • (1992) Phys. Rev. A. , vol.45 , pp. 7058
    • Martinerie, J.M.1    Albano, A.M.2    Mees, A.I.3    Rapp, P.E.4
  • 42
    • 26544461279 scopus 로고
    • Reconstruction expansion as a geometrybased framework for choosing proper delay times
    • M. T. Rosenstein, J. J. Collins, and C. J. de Luca, Reconstruction expansion as a geometrybased framework for choosing proper delay times. Physica D 73: 82-98, 1994.
    • (1994) Physica D , vol.73 , pp. 82-98
    • Rosenstein, M.T.1    Collins, J.J.2    De Luca, C.J.3
  • 43
    • 0001394076 scopus 로고
    • Measurement of the Lyapunov spectrum from a chaotic time series
    • M. Sano and Y. Sawada, Measurement of the Lyapunov spectrum from a chaotic time series. Phys. Rev. Lett. 55: 1082-1085, 1985.
    • (1985) Phys. Rev. Lett. , vol.55 , pp. 1082-1085
    • Sano, M.1    Sawada, Y.2
  • 44
    • 43949166788 scopus 로고
    • A practical method for calculating largest Lyapunov exponents from small data sets
    • M. T. Rosenstein, J. J. Collins, and C. J. de Luca, A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65: 117-134, 1994.
    • (1994) Physica D , vol.65 , pp. 117-134
    • Rosenstein, M.T.1    Collins, J.J.2    De Luca, C.J.3
  • 45
  • 46
  • 48
    • 12044259811 scopus 로고
    • Where can one hope to profitably apply the ideas of chaos?
    • July
    • D. Ruelle, Where can one hope to profitably apply the ideas of chaos? Phys. Today July: 2430, 1994.
    • (1994) Phys. Today , pp. 2430
    • Ruelle, D.1
  • 49
    • 0001033183 scopus 로고
    • Construction and analysis of differential equations from experimental time series of oscillatory systems
    • B. R. Noack, F. Ohle, and H. Eckelmann, Construction and analysis of differential equations from experimental time series of oscillatory systems. Physica D 56: 389-405, 1992.
    • (1992) Physica D , vol.56 , pp. 389-405
    • Noack, B.R.1    Ohle, F.2    Eckelmann, H.3
  • 50
    • 0002972668 scopus 로고
    • Controlling chaos
    • May
    • E. Ott and M. Spano, Controlling chaos. Phys. Today May: 34-40, 1995.
    • (1995) Phys. Today , pp. 34-40
    • Ott, E.1    Spano, M.2


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