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Volumn 5, Issue 1, 1997, Pages 33-52

Estimating correlation dimensions of biological time series with a reliable method

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EID: 21444458135     PISSN: 10641246     EISSN: None     Source Type: Journal    
DOI: 10.3233/ifs-1997-5104     Document Type: Article
Times cited : (24)

References (44)
  • 1
    • 35949011725 scopus 로고
    • Singular-value decomposition and the Grassberger-Procaccia algorithm
    • Albano AM, Muench J, Schwartz C, Mees AI (1988): "Singular-value decomposition and the Grassberger-Procaccia algorithm." Phys. Rev. A, 38: 3017-3026.
    • (1988) Phys. Rev. A , vol.38 , pp. 3017-3026
    • Albano, A.M.1    Muench, J.2    Schwartz, C.3    Mees, A.I.4
  • 2
    • 0002064172 scopus 로고
    • Using higher order correlations to define an embedding window
    • Albano AM, Passamante A, Farrell ME (1991): "Using higher order correlations to define an embedding window." Physica D 54: 81-97.
    • (1991) Physica D , vol.54 , pp. 81-97
    • Albano, A.M.1    Passamante, A.2    Farrell, M.E.3
  • 3
    • 0002615297 scopus 로고
    • Détermination de dimension d'attracteurs pour différents écoulements
    • Atten P, Caputo JG, Malraison B, Gagne Y (1984): "Détermination de dimension d'attracteurs pour différents écoulements." J. Mécan. Théor. Appli. 156: 133-156.
    • (1984) J. Mécan. Théor. Appli. , vol.156 , pp. 133-156
    • Atten, P.1    Caputo, J.G.2    Malraison, B.3    Gagne, Y.4
  • 4
    • 38249002177 scopus 로고
    • Entropy profiles of speech signals
    • Bandt C, Pompe B (1993): "Entropy profiles of speech signals." Phys. Lett. A 175: 305-313.
    • (1993) Phys. Lett. A , vol.175 , pp. 305-313
    • Bandt, C.1    Pompe, B.2
  • 5
    • 0001582848 scopus 로고
    • Discussion on the spectral analysis of point process [by MS Bartlett]
    • Barnard GA (1963): "Discussion on the spectral analysis of point process [by MS Bartlett]." J. R. Stat. Soc. B 25: 294.
    • (1963) J. R. Stat. Soc. B , vol.25 , pp. 294
    • Barnard, G.A.1
  • 6
    • 0000712818 scopus 로고
    • Multidimensional trees, range searching, and a correlation dimension algorithm of reduced complexity
    • Bingham S, Kot M (1989): "Multidimensional trees, range searching, and a correlation dimension algorithm of reduced complexity." Phys. Lett. A 140: 327-330.
    • (1989) Phys. Lett. A , vol.140 , pp. 327-330
    • Bingham, S.1    Kot, M.2
  • 7
    • 34249988665 scopus 로고
    • Extracting qualitative dynamics from experimental data
    • Broomhead DS, King GP (1986): "Extracting qualitative dynamics from experimental data." Physica, 20D: 217-236.
    • (1986) Physica , vol.20 D , pp. 217-236
    • Broomhead, D.S.1    King, G.P.2
  • 8
    • 44049113708 scopus 로고
    • Comparison of algorithms calculating optimal embedding parameters for delay time coordinates
    • Buzug T, Pfister G (1992): "Comparison of algorithms calculating optimal embedding parameters for delay time coordinates." Physica D 58: 127-137.
    • (1992) Physica D , vol.58 , pp. 127-137
    • Buzug, T.1    Pfister, G.2
  • 9
    • 84956277039 scopus 로고
    • Optimal reconstruction of strange attractors from purely geometrical arguments
    • Buzug T, Reimers T, Pfister G (1990): "Optimal reconstruction of strange attractors from purely geometrical arguments." Europhys. Lett. 13: 605-610.
    • (1990) Europhys. Lett. , vol.13 , pp. 605-610
    • Buzug, T.1    Reimers, T.2    Pfister, G.3
  • 10
    • 45149144372 scopus 로고
    • Nonlinear prediction of chaotic time series
    • Casdagli M (1989): "Nonlinear prediction of chaotic time series." Physica D 35: 335-356.
    • (1989) Physica D , vol.35 , pp. 335-356
    • Casdagli, M.1
  • 11
    • 44949273552 scopus 로고
    • State space reconstruction in the presence of noise
    • Casdagli M, Eubank S, Farmer JD, Gibson J (1991): "State space reconstruction in the presence of noise." Physica D 51: 52-98.
    • (1991) Physica D , vol.51 , pp. 52-98
    • Casdagli, M.1    Eubank, S.2    Farmer, J.D.3    Gibson, J.4
  • 13
    • 0000805857 scopus 로고
    • Modification of the Grass-berger-Procaccia algorithm for estimating the correlation exponent of chaotic systems with high embedding dimension
    • Dvorak I, Klaschka J (1990): "Modification of the Grass-berger-Procaccia algorithm for estimating the correlation exponent of chaotic systems with high embedding dimension." Phys. Lett. A 145: 225-231.
    • (1990) Phys. Lett. A , vol.145 , pp. 225-231
    • Dvorak, I.1    Klaschka, J.2
  • 15
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors
    • Eckmann JP, Ruelle D (1985): "Ergodic theory of chaos and strange attractors." Rev. Mod. Physica. 57: 617-656.
    • (1985) Rev. Mod. Physica. , vol.57 , pp. 617-656
    • Eckmann, J.P.1    Ruelle, D.2
  • 16
    • 44049117207 scopus 로고
    • Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems
    • Eckmann JP, Ruelle D (1992): "Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems." Physica D 56: 185-187.
    • (1992) Physica D , vol.56 , pp. 185-187
    • Eckmann, J.P.1    Ruelle, D.2
  • 17
    • 0000592333 scopus 로고
    • Estimating attractor dimensions from limited data: A new method, with error estimates
    • Ellener S (1988): "Estimating attractor dimensions from limited data: A new method, with error estimates." Phys. Lett. A 133: 128-133.
    • (1988) Phys. Lett. A , vol.133 , pp. 128-133
    • Ellener, S.1
  • 19
    • 0002635074 scopus 로고
    • Exploiting chaos to predict the future and reduce noise
    • Lee YC (ed): Singapore: World Scientific
    • Farmer JD, Sidorowich JJ (1988): "Exploiting chaos to predict the future and reduce noise." In Lee YC (ed): Evolution Learning and Cognition. Singapore: World Scientific, pp. 277-330.
    • (1988) Evolution Learning and Cognition , pp. 277-330
    • Farmer, J.D.1    Sidorowich, J.J.2
  • 20
    • 0024627335 scopus 로고
    • Information and entropy in strange attractors
    • Fraser AM (1989a): "Information and entropy in strange attractors." IEEE Trans. Inf. Theory 35: 245-262.
    • (1989) IEEE Trans. Inf. Theory , vol.35 , pp. 245-262
    • Fraser, A.M.1
  • 21
    • 0001628622 scopus 로고
    • Reconstructing attractors from scalar time series: A comparison of singular system and redundancy criteria
    • Fraser AM (1989b): "Reconstructing attractors from scalar time series: A comparison of singular system and redundancy criteria." Physica D 34: 391-404.
    • (1989) Physica D , vol.34 , pp. 391-404
    • Fraser, A.M.1
  • 22
    • 10944271477 scopus 로고
    • Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time series
    • Gao J, Zheng Z (1994): "Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time series." Phys. Rev. E 49: 3807-3814.
    • (1994) Phys. Rev. E , vol.49 , pp. 3807-3814
    • Gao, J.1    Zheng, Z.2
  • 23
    • 0000090102 scopus 로고
    • Finite sample corrections to entropy and dimension estimates
    • Grassberger P (1988): "Finite sample corrections to entropy and dimension estimates." Phys. Lett. A 128: 369-373.
    • (1988) Phys. Lett. A , vol.128 , pp. 369-373
    • Grassberger, P.1
  • 24
    • 5544314929 scopus 로고
    • An optimized box-assisted algorithm for fractal dimensions
    • Grassberger P (1990): "An optimized box-assisted algorithm for fractal dimensions." Phys. Lett. A 148: 63-68.
    • (1990) Phys. Lett. A , vol.148 , pp. 63-68
    • Grassberger, P.1
  • 25
    • 40749093037 scopus 로고
    • Measuring the strangeness of strange attractors
    • Grassberger P, Procaccia I (1983a): "Measuring the strangeness of strange attractors." Physica D 9: 189-208.
    • (1983) Physica D , vol.9 , pp. 189-208
    • Grassberger, P.1    Procaccia, I.2
  • 26
    • 33646981873 scopus 로고
    • Characterization of strange attractors
    • Grassberger P, Procaccia I (1983b): "Characterization of strange attractors." Phys. Rev. Lett. 50: 346-349.
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 346-349
    • Grassberger, P.1    Procaccia, I.2
  • 28
    • 0002002528 scopus 로고
    • A simplified Monte Carlo significance test procedure
    • Hope ACA (1968): "A simplified Monte Carlo significance test procedure." J. R. Stat. Soc. B 30: 582-598.
    • (1968) J. R. Stat. Soc. B , vol.30 , pp. 582-598
    • Hope, A.C.A.1
  • 31
    • 0000633768 scopus 로고
    • An improved estimation of dimension and some comments on providing confidence intervals
    • Judd K (1992): "An improved estimation of dimension and some comments on providing confidence intervals." Physica D 56: 216-228.
    • (1992) Physica D , vol.56 , pp. 216-228
    • Judd, K.1
  • 32
    • 43949148645 scopus 로고
    • Estimating dimension from small samples
    • Judd K (1994): "Estimating dimension from small samples." Physica D 71: 421-429.
    • (1994) Physica D , vol.71 , pp. 421-429
    • Judd, K.1
  • 33
    • 8044250325 scopus 로고
    • Estimating dimensions with confidence
    • Judd K, Mees AI (1991): "Estimating dimensions with confidence." Int. J. Bifurc. Chaos 1: 467-470.
    • (1991) Int. J. Bifurc. Chaos , vol.1 , pp. 467-470
    • Judd, K.1    Mees, A.I.2
  • 34
    • 38249014976 scopus 로고
    • Random sampling and the Grassberger-Procaccia algorithm
    • Kember G, Fowler AC (1992): "Random sampling and the Grassberger-Procaccia algorithm." Phys. Lett. A 161: 429-432.
    • (1992) Phys. Lett. A , vol.161 , pp. 429-432
    • Kember, G.1    Fowler, A.C.2
  • 35
    • 0002227785 scopus 로고
    • A correlation function for choosing time delays in phase portrait reconstructions
    • Kember G, Fowler AC (1993): "A correlation function for choosing time delays in phase portrait reconstructions." Phys. Lett. A 179(2):72-80.
    • (1993) Phys. Lett. A , vol.179 , Issue.2 , pp. 72-80
    • Kember, G.1    Fowler, A.C.2
  • 36
    • 0003145759 scopus 로고
    • Phase portraits from a time series: A singular system approach
    • King GP, Jones R, Broomhead DS (1987): "Phase portraits from a time series: A singular system approach." Nuclear Phys. B 2:379.
    • (1987) Nuclear Phys. B , vol.2 , pp. 379
    • King, G.P.1    Jones, R.2    Broomhead, D.S.3
  • 37
    • 84956258433 scopus 로고
    • Optimal embeddings of chaotic attractors from topological considerations
    • Liebert W, Paweilzik K, Shuster HG (1991): "Optimal embeddings of chaotic attractors from topological considerations." Europhys. Lett. 14: 521-526.
    • (1991) Europhys. Lett. , vol.14 , pp. 521-526
    • Liebert, W.1    Paweilzik, K.2    Shuster, H.G.3
  • 38
    • 30244464950 scopus 로고
    • Proper choice of the time delay for the analysis of chaotic time series
    • Liebert W, Schuster HG (1989): "Proper choice of the time delay for the analysis of chaotic time series." Phys. Lett. A 142: 107-111.
    • (1989) Phys. Lett. A , vol.142 , pp. 107-111
    • Liebert, W.1    Schuster, H.G.2
  • 39
    • 0003290175 scopus 로고
    • On the dimension of the compact invariant sets of certain non-linear maps
    • Rand DA, Young BS (eds): Berlin: Springer-Verlag
    • Mañé R. (1981): "On the dimension of the compact invariant sets of certain non-linear maps." In Rand DA, Young BS (eds): Dynamical Systems of Turbulence. Vol. 898 of Lecture Notes in Mathematics, Berlin: Springer-Verlag, pp. 230-242.
    • (1981) Dynamical Systems of Turbulence. Vol. 898 of Lecture Notes in Mathematics , vol.898 , pp. 230-242
    • Mañé, R.1
  • 40
    • 0000611452 scopus 로고
    • Dynamical systems and tesslations: Detecting determinism in data
    • Mees AI (1991): "Dynamical systems and tesslations: Detecting determinism in data." Int. J. Bifurc. Chaos 1: 777-794.
    • (1991) Int. J. Bifurc. Chaos , vol.1 , pp. 777-794
    • Mees, A.I.1
  • 41
    • 35949015106 scopus 로고
    • Singular-value decomposition and embedding dimension
    • Mees AI, Rapp PE, Jennings LE (1987): "Singular-value decomposition and embedding dimension." Phys. Rev. A 36: 340-346.
    • (1987) Phys. Rev. A , vol.36 , pp. 340-346
    • Mees, A.I.1    Rapp, P.E.2    Jennings, L.E.3
  • 42
    • 0000801812 scopus 로고
    • Bifurcation and chaos in newborn infant cries
    • Mende W, Herzel H, Wermke K (1990): "Bifurcation and chaos in newborn infant cries." Phys. Lett. A 145: 418-424.
    • (1990) Phys. Lett. A , vol.145 , pp. 418-424
    • Mende, W.1    Herzel, H.2    Wermke, K.3
  • 43
    • 0011198007 scopus 로고
    • A maximum likelihood approach to correlation dimension and entropy function
    • Olofen E, Degoede J, Heijungs R (1992): "A maximum likelihood approach to correlation dimension and entropy function." Bull. Math. Biol. 54: 45-58.
    • (1992) Bull. Math. Biol. , vol.54 , pp. 45-58
    • Olofen, E.1    Degoede, J.2    Heijungs, R.3
  • 44
    • 5544310124 scopus 로고
    • Finite correlation dimension for stochastic systems with power-law spectra
    • Osborne AR, Provenzale A (1989): "Finite correlation dimension for stochastic systems with power-law spectra." Physica D 35: 357-381.
    • (1989) Physica D , vol.35 , pp. 357-381
    • Osborne, A.R.1    Provenzale, A.2


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