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Volumn 126, Issue 1-2, 1999, Pages 49-59

The bootstrap and Lyapunov exponents in deterministic chaos

Author keywords

Bootstrap; Chaos; Dynamical noise; Lyapunov exponent; Nonlinear systems; Observational noise; Uncertainty

Indexed keywords


EID: 0038847742     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00256-5     Document Type: Article
Times cited : (39)

References (54)
  • 1
    • 0003495086 scopus 로고
    • Accademia Nazionale Dei Lincei, Cambridge University Press, Cambridge
    • D. Ruelle, Chaotic Evolution and Strange Attractors, Accademia Nazionale Dei Lincei, Cambridge University Press, Cambridge, 1989.
    • (1989) Chaotic Evolution and Strange Attractors
    • Ruelle, D.1
  • 2
    • 0001062715 scopus 로고    scopus 로고
    • A statistical framework for testing chaotic dynamics via Lyapunov exponents
    • Gençay R. A statistical framework for testing chaotic dynamics via Lyapunov exponents. Physica D. 89:1996;261-266.
    • (1996) Physica D , vol.89 , pp. 261-266
    • Gençay, R.1
  • 3
    • 0001036009 scopus 로고
    • A study of the predictability of a 28-variable atmospheric model
    • Lorenz E.N. A study of the predictability of a 28-variable atmospheric model. Tellus. 17:1965;321-333.
    • (1965) Tellus , vol.17 , pp. 321-333
    • Lorenz, E.N.1
  • 4
    • 0000181737 scopus 로고
    • The jackknife and the bootstrap for general stationary observations
    • Künsch H.R. The jackknife and the bootstrap for general stationary observations. Ann. of Stat. 17(3):1989;1217-1241.
    • (1989) Ann. of Stat. , vol.17 , Issue.3 , pp. 1217-1241
    • Künsch, H.R.1
  • 5
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors
    • Eckmann J.-P., Ruelle D. Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57:1985;617-656.
    • (1985) Rev. Mod. Phys. , vol.57 , pp. 617-656
    • Eckmann, J.-P.1    Ruelle, D.2
  • 7
    • 0000974708 scopus 로고
    • Local optimal prediction: Exploiting strangeness and the variation of sensitivity to initial condition
    • Smith L.A. Local optimal prediction: exploiting strangeness and the variation of sensitivity to initial condition. Phil. Trans. R. Soc. London A. 348(1688):1994;371-381.
    • (1994) Phil. Trans. R. Soc. London a , vol.348 , Issue.1688 , pp. 371-381
    • Smith, L.A.1
  • 8
    • 4243347660 scopus 로고    scopus 로고
    • Towards confindence estimates for Lyapunov exponents
    • in preparation
    • L.A. Smith, C. Ziehmann, J. Kurths, Towards confindence estimates for Lyapunov exponents, Physica D, in preparation.
    • Physica D
    • Smith, L.A.1    Ziehmann, C.2    Kurths, J.3
  • 9
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems
    • Oseledec V.I. A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19:1968;197-231.
    • (1968) Trans. Moscow Math. Soc. , vol.19 , pp. 197-231
    • Oseledec, V.I.1
  • 10
    • 0001731208 scopus 로고
    • Lyapunov exponents in chaotic systems: Their importance and their evaluation using observed data
    • Abarbanel H.D.I., Brown R., Kennel M.B. Lyapunov exponents in chaotic systems: their importance and their evaluation using observed data. Int. J. Mod. Phys. B. 5:1991;1347-1375.
    • (1991) Int. J. Mod. Phys. B , vol.5 , pp. 1347-1375
    • Abarbanel, H.D.I.1    Brown, R.2    Kennel, M.B.3
  • 12
    • 0000670905 scopus 로고
    • Accountability and error in ensemble prediction
    • European Centre for Medium-Range Weather Forecasts, September
    • L.A. Smith, Accountability and error in ensemble prediction, in: Predictability, vol. 1, Seminar Proceeding, European Centre for Medium-Range Weather Forecasts, September 1995, pp. 351-368.
    • (1995) In: Predictability, Vol. 1, Seminar Proceeding , pp. 351-368
    • Smith, L.A.1
  • 13
    • 0002141262 scopus 로고    scopus 로고
    • Uncertainty dynamics and predictability in chaotic systems
    • in review
    • L.A. Smith, C. Ziehmann, K. Fraedrich, Uncertainty dynamics and predictability in chaotic systems, Q.J.R. Meterol. Soc. (1998), in review.
    • (1998) Q.J.R. Meterol. Soc.
    • Smith, L.A.1    Ziehmann, C.2    Fraedrich, K.3
  • 14
    • 0029412335 scopus 로고
    • The singular-vector structure of the atmospheric global circulation
    • Buizza R., Palmer T.N. The singular-vector structure of the atmospheric global circulation. J. Atmos. Sci. 52(9):1995;1434-1455.
    • (1995) J. Atmos. Sci. , vol.52 , Issue.9 , pp. 1434-1455
    • Buizza, R.1    Palmer, T.N.2
  • 15
    • 35949037738 scopus 로고
    • Kolmogorov entropy and numerical experiments
    • Benettin G., Galgani L., Strelcyn J.-M. Kolmogorov entropy and numerical experiments. Phys. Rev. A. 14:1976;2338-2345.
    • (1976) Phys. Rev. a , vol.14 , pp. 2338-2345
    • Benettin, G.1    Galgani, L.2    Strelcyn, J.-M.3
  • 16
    • 0000672504 scopus 로고
    • A numerical approach to ergodic problem in dissipative dynamical systems
    • Shimada I., Nagashima T. A numerical approach to ergodic problem in dissipative dynamical systems. Prog. Theoret. Phys. 61:1979;1605-1616.
    • (1979) Prog. Theoret. Phys. , vol.61 , pp. 1605-1616
    • Shimada, I.1    Nagashima, T.2
  • 17
    • 0000339553 scopus 로고
    • The calculation of Lyapunov spectra
    • Greene J.M., Kim J.-S. The calculation of Lyapunov spectra. Physica. D24:1987;213-225.
    • (1987) Physica , vol.24 , pp. 213-225
    • Greene, J.M.1    Kim, J.-S.2
  • 18
    • 0008494528 scopus 로고
    • Determining Lyapunov exponents from a time series
    • Wolf A., Swift J.B., Swinney H.L., Vastano J.A. Determining Lyapunov exponents from a time series. Physica. D16:1985;285-317.
    • (1985) Physica , vol.16 , pp. 285-317
    • Wolf, A.1    Swift, J.B.2    Swinney, H.L.3    Vastano, J.A.4
  • 19
    • 0001394076 scopus 로고
    • Measurement of the Lyapunov spectrum from a chaotic time series
    • Sano M., Sawada Y. Measurement of the Lyapunov spectrum from a chaotic time series. Phys. Rev. Lett. 55:1985;1082-1085.
    • (1985) Phys. Rev. Lett. , vol.55 , pp. 1082-1085
    • Sano, M.1    Sawada, Y.2
  • 21
    • 0001571275 scopus 로고
    • An attractor in a solar time series
    • Kurths J., Herzel H. An attractor in a solar time series. Physica D. 25:1987;165-172.
    • (1987) Physica D , vol.25 , pp. 165-172
    • Kurths, J.1    Herzel, H.2
  • 22
    • 35949009462 scopus 로고
    • Computing the Lyapunov spectrum of dynamical system from an observed time series
    • Brown R., Bryant P., Abarbanel H.D.I. Computing the Lyapunov spectrum of dynamical system from an observed time series. Phys. Rev. A. 43(6):1991;2787-2806.
    • (1991) Phys. Rev. a , vol.43 , Issue.6 , pp. 2787-2806
    • Brown, R.1    Bryant, P.2    Abarbanel, H.D.I.3
  • 23
    • 0000905883 scopus 로고
    • Identification of true and spurious Lyapunov exponents
    • Parlitz U. Identification of true and spurious Lyapunov exponents. Int. J. Bifur. Chaos. 2:1992;155.
    • (1992) Int. J. Bifur. Chaos , vol.2 , pp. 155
    • Parlitz, U.1
  • 25
    • 0000610143 scopus 로고    scopus 로고
    • Robust estimation of tangent maps and Lyapunov spectra
    • Darbyshire A.G., Broomhead D.S. Robust estimation of tangent maps and Lyapunov spectra. Physica D. 89:1996;287-305.
    • (1996) Physica D , vol.89 , pp. 287-305
    • Darbyshire, A.G.1    Broomhead, D.S.2
  • 26
    • 0002591468 scopus 로고
    • A two-dimensional map with a strange attractor
    • Henon M. A two-dimensional map with a strange attractor. Commun. Math. Phys. 50:1976;69.
    • (1976) Commun. Math. Phys. , vol.50 , pp. 69
    • Henon, M.1
  • 27
    • 0002479384 scopus 로고    scopus 로고
    • Testing chaotic dynamics via Lyapunov exponents
    • Bask M., Gençay R. Testing chaotic dynamics via Lyapunov exponents. Physica D. 114:1998;1-2.
    • (1998) Physica D , vol.114 , pp. 1-2
    • Bask, M.1    Gençay, R.2
  • 28
    • 0018508810 scopus 로고
    • Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system.
    • Ikeda K. Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Opt. Commun. 30:1979;257.
    • (1979) Opt. Commun. , vol.30 , pp. 257
    • Ikeda, K.1
  • 29
    • 0001414087 scopus 로고
    • Convergence rates and data requirements for the Jacobian-based estinmates of Lyapunov exponents
    • Ellner S., Gallant R., McGaffrey D., Nychka D. Convergence rates and data requirements for the Jacobian-based estinmates of Lyapunov exponents. Phys. Lett. A. 153:1991;357-363.
    • (1991) Phys. Lett. a , vol.153 , pp. 357-363
    • Ellner, S.1    Gallant, R.2    McGaffrey, D.3    Nychka, D.4
  • 30
    • 84956071330 scopus 로고
    • Gibbs measures in ergodic theory
    • Sinai Ya.G. Gibbs measures in ergodic theory. Russian Math. Surveys. 27(4)(4):1972;768.
    • (1972) Russian Math. Surveys , vol.274 , Issue.4 , pp. 768
    • Sinai, Ya.g.1
  • 34
    • 84964203940 scopus 로고
    • Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy
    • Efron B., Tibshirani R. Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statist. Sci. 1(1):1986;57-77.
    • (1986) Statist. Sci. , vol.1 , Issue.1 , pp. 57-77
    • Efron, B.1    Tibshirani, R.2
  • 36
    • 0012349493 scopus 로고
    • Crisis, sudden changes in chaotic attractors, and transient chaos
    • Grebogi C., Ott E., Yorke J.A. Crisis, sudden changes in chaotic attractors, and transient chaos. Physica D. 7:1983;181-200.
    • (1983) Physica D , vol.7 , pp. 181-200
    • Grebogi, C.1    Ott, E.2    Yorke, J.A.3
  • 37
    • 0040922503 scopus 로고
    • Ordinary differential equations with strange attractors
    • (transient choas to limit cycle)
    • C.J. Marzec, E.A. Spiegel, Ordinary differential equations with strange attractors, SIAM J. Appl. Math. 38 (1980) 387 (transient choas to limit cycle).
    • (1980) SIAM J. Appl. Math. , vol.38 , pp. 387
    • Marzec, C.J.1    Spiegel, E.A.2
  • 38
    • 0000313555 scopus 로고
    • Quantifying local predictability in phase
    • Nese J.M. Quantifying local predictability in phase. Physica D. 35:1989;237-250.
    • (1989) Physica D , vol.35 , pp. 237-250
    • Nese, J.M.1
  • 39
    • 84949405337 scopus 로고
    • Non-uniform chaotic dynamics with implications to information processing
    • J.S. Nicolis, G. Meyer-Kress, G. Haubs, Non-uniform chaotic dynamics with implications to information processing, Zeitschrift für Naturforschung 38a (1983) 1157-1169.
    • (1983) Zeitschrift für Naturforschung , vol.38 A , pp. 1157-1169
    • Nicolis, J.S.1    Meyer-Kress, G.2    Haubs, G.3
  • 40
    • 0039262091 scopus 로고
    • Lyapunov exponents for hydromagnetic convection
    • J. Kurths, A. Brandenburg, Lyapunov exponents for hydromagnetic convection, Phys. Rev. A 44 (1991) R3427-R3429.
    • (1991) Phys. Rev. a , vol.44
    • Kurths, J.1    Brandenburg, A.2
  • 41
    • 0000339204 scopus 로고
    • Variation of Lyapunov exponents on a strange attractor
    • Abarbanel H.D.I., Brown R., Kennel M.B. Variation of Lyapunov exponents on a strange attractor. J. Nonlinear Sci. 1:1991;175-199.
    • (1991) J. Nonlinear Sci. , vol.1 , pp. 175-199
    • Abarbanel, H.D.I.1    Brown, R.2    Kennel, M.B.3
  • 43
    • 0026302232 scopus 로고
    • A relationship between local error growth and quasi-stationary states: Case study in the Lorenz system
    • Mukougawa H., Kimoto M., Yoden S. A relationship between local error growth and quasi-stationary states: Case study in the Lorenz system. J. Atmos. Sci. 48:1991;1231-1237.
    • (1991) J. Atmos. Sci. , vol.48 , pp. 1231-1237
    • Mukougawa, H.1    Kimoto, M.2    Yoden, S.3
  • 44
    • 0027799457 scopus 로고
    • Finite-time Lyapunov stability analysis and its application to atmospheric dynamics
    • Yoden S., Nomura M. Finite-time Lyapunov stability analysis and its application to atmospheric dynamics. J. Atmos. Sci. 50:1993;1531-1543.
    • (1993) J. Atmos. Sci. , vol.50 , pp. 1531-1543
    • Yoden, S.1    Nomura, M.2
  • 45
    • 23944441372 scopus 로고
    • Strange non-chaotic attractor in a quasiperiodically forced circle map
    • Feudel U., Kurths J., Pikovsky A. Strange non-chaotic attractor in a quasiperiodically forced circle map. Physica D. 88:1995;176-186.
    • (1995) Physica D , vol.88 , pp. 176-186
    • Feudel, U.1    Kurths, J.2    Pikovsky, A.3
  • 46
    • 0027008834 scopus 로고
    • Probabilistic aspects of error growth in atmospheric dynamics
    • Nicolis C. Probabilistic aspects of error growth in atmospheric dynamics. Q.J.R. Meteorol. Soc. 118:1992;553-568.
    • (1992) Q.J.R. Meteorol. Soc. , vol.118 , pp. 553-568
    • Nicolis, C.1
  • 47
    • 33750490125 scopus 로고
    • Local Lyapunov exponents in chaotic systems
    • Eckhardt B., Yao D. Local Lyapunov exponents in chaotic systems. Physica D. 65:1993;100-108.
    • (1993) Physica D , vol.65 , pp. 100-108
    • Eckhardt, B.1    Yao, D.2
  • 48
    • 0028975202 scopus 로고
    • Short-range predictability of the atmosphere: Mechanism for superexponential error growth
    • Nicolis C., Vannitsem S., Royer J.-F. Short-range predictability of the atmosphere: mechanism for superexponential error growth. Q.J.R. Meteorol. Soc. 121:1995;705-722.
    • (1995) Q.J.R. Meteorol. Soc. , vol.121 , pp. 705-722
    • Nicolis, C.1    Vannitsem, S.2    Royer, J.-F.3
  • 49
    • 0028831683 scopus 로고
    • Transient error growth and local predictability: A study in the Lorenz system
    • Trevisan A., Legnani R. Transient error growth and local predictability: a study in the Lorenz system. Tellus. A47:1995;103-117.
    • (1995) Tellus , vol.47 , pp. 103-117
    • Trevisan, A.1    Legnani, R.2
  • 50
    • 0001509508 scopus 로고
    • Ensemble Forecasting at NMC: The generation of perturbations
    • Toth Z., Kalnay E. Ensemble Forecasting at NMC: The generation of perturbations. Bull. Amer. Meteorol. Soc. 74(12):1993;2317-2330.
    • (1993) Bull. Amer. Meteorol. Soc. , vol.74 , Issue.12 , pp. 2317-2330
    • Toth, Z.1    Kalnay, E.2
  • 51
    • 0001419994 scopus 로고
    • Quantifying the influence of initial values Nonlinear prediction
    • Yao Q., Tong H. Quantifying the influence of initial values Nonlinear prediction. J. R. Statist. Soc. B. 56(4):1994;701-725.
    • (1994) J. R. Statist. Soc. B , vol.56 , Issue.4 , pp. 701-725
    • Yao, Q.1    Tong, H.2
  • 53
    • 0012953052 scopus 로고
    • Anomalous convergence of Lyapunov exponent estimates
    • Theiler J., Smith L.A. Anomalous convergence of Lyapunov exponent estimates. Phys. Rev. E. 51:1995;3738-3741.
    • (1995) Phys. Rev. e , vol.51 , pp. 3738-3741
    • Theiler, J.1    Smith, L.A.2
  • 54
    • 0003882610 scopus 로고
    • (translated by R. Bartels, W. Gautschi, C. Witzgall), Springer, New York
    • J. Stoer, R. Burlisch, Introduction to Numerical Analysis (translated by R. Bartels, W. Gautschi, C. Witzgall), Springer, New York, 1980.
    • (1980) Introduction to Numerical Analysis
    • Stoer, J.1    Burlisch, R.2


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