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Volumn 13, Issue 6, 2003, Pages 1383-1422

Recent developments in chaotic time series analysis

Author keywords

Chaotic time series; Correlation dimension; Delay coordinates; Embedding; Hiebert transform; Instantaneous frequency; Lyapunov exponents; Transient chaos; Unstable periodic orbits

Indexed keywords

COMPUTATIONAL METHODS; CORRELATION METHODS; FRACTALS; LYAPUNOV METHODS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR SYSTEMS; TIME SERIES ANALYSIS;

EID: 0042379778     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127403007308     Document Type: Review
Times cited : (86)

References (124)
  • 2
    • 0000761266 scopus 로고    scopus 로고
    • Finding periodic points from short time series
    • Allie, S. & Mees, A. [1997] "Finding periodic points from short time series," Phys. Rev. E56, 346-350.
    • (1997) Phys. Rev. , vol.E56 , pp. 346-350
    • Allie, S.1    Mees, A.2
  • 3
    • 0000472945 scopus 로고    scopus 로고
    • Noise scaling in phase synchronization of coupled chaotic oscillators
    • Andrade, V., Davidchack, R. L. & Lai, Y.-C. [2000] "Noise scaling in phase synchronization of coupled chaotic oscillators," Phys. Rev. E61, 3230-3233.
    • (2000) Phys. Rev. , vol.E61 , pp. 3230-3233
    • Andrade, V.1    Davidchack, R.L.2    Lai, Y.-C.3
  • 4
    • 0035488686 scopus 로고    scopus 로고
    • Super persistent chaotic transients in physical systems: Effect of noise on phase synchronization of coupled chaotic oscillators
    • Andrade, V. & Lai, Y.-C. [2001] "Super persistent chaotic transients in physical systems: Effect of noise on phase synchronization of coupled chaotic oscillators," Int. J. Bifurcation and Chaos 11, 2607-2619.
    • (2001) Int. J. Bifurcation and Chaos , vol.11 , pp. 2607-2619
    • Andrade, V.1    Lai, Y.-C.2
  • 8
    • 84938451367 scopus 로고
    • A product theorem for Hilbert transform
    • Bedrosian, E. [1963] "A product theorem for Hilbert transform, " Proc. IEEE 51, 868-869.
    • (1963) Proc. IEEE , vol.51 , pp. 868-869
    • Bedrosian, E.1
  • 9
    • 0018992908 scopus 로고
    • Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them. Part 2: Numerical application
    • Benettin, G., Galgani, L., Giorgilli, A. & Strelcyn, J. M. [1980] "Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them. Part 2: Numerical application," Meccanica 15, p. 21.
    • (1980) Meccanica , vol.15 , pp. 21
    • Benettin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.M.4
  • 10
    • 0001452580 scopus 로고
    • Characterization of unstable periodic orbits in chaotic attractors and repellers
    • Biham, O. & Wenzel, W. [1989] "Characterization of unstable periodic orbits in chaotic attractors and repellers," Phys. Rev. Lett. 63, 819-822.
    • (1989) Phys. Rev. Lett. , vol.63 , pp. 819-822
    • Biham, O.1    Wenzel, W.2
  • 11
    • 84937035392 scopus 로고
    • Estimating and interpreting the instantaneous frequency of a signal, I. Fundamentals
    • Boashash, B. [1992] "Estimating and interpreting the instantaneous frequency of a signal, I. Fundamentals," Proc. IEEE 80, 520-538.
    • (1992) Proc. IEEE , vol.80 , pp. 520-538
    • Boashash, B.1
  • 14
    • 35949009462 scopus 로고
    • Computing the Lyapunov spectrum of a dynamical system from an observed time series
    • Brown, R., Bryant, P. & Abarbanel, H. D. I. [1991] "Computing the Lyapunov spectrum of a dynamical system from an observed time series," Phys. Rev. A43, 2787-2806.
    • (1991) Phys. Rev. , vol.A43 , pp. 2787-2806
    • Brown, R.1    Bryant, P.2    Abarbanel, H.D.I.3
  • 15
    • 0000805615 scopus 로고
    • Optimal delay time and embedding dimension for delay-time coordinates by analysis of the glocal static and local dynamic behavior of strange attractors
    • Buzug, T. & Pfister, G. [1992] "Optimal delay time and embedding dimension for delay-time coordinates by analysis of the glocal static and local dynamic behavior of strange attractors," Phys. Rev. A45, 7073-7084.
    • (1992) Phys. Rev. , vol.A45 , pp. 7073-7084
    • Buzug, T.1    Pfister, G.2
  • 17
    • 0002870373 scopus 로고
    • Calculating topological entropies of chaotic dynamical systems
    • Chen, Q., Ott, E. & Hurd, L. P. [1991] "Calculating topological entropies of chaotic dynamical systems," Phys. Lett. A156, 48-52.
    • (1991) Phys. Lett. , vol.A156 , pp. 48-52
    • Chen, Q.1    Ott, E.2    Hurd, L.P.3
  • 19
    • 0000152926 scopus 로고
    • Controlling nonchaotic neuronal noise using chaos control techniques
    • Christini, D. J. & Collins, J. J. [1995] "Controlling nonchaotic neuronal noise using chaos control techniques," Phys. Rev. Lett. 75, 2782-2785.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 2782-2785
    • Christini, D.J.1    Collins, J.J.2
  • 20
    • 0001611630 scopus 로고    scopus 로고
    • Efficient algorithm for detecting unstable periodic orbits in chaotic systems
    • Davidchack, R. L. & Lai, Y. C. [1999] "Efficient algorithm for detecting unstable periodic orbits in chaotic systems," Phys. Rev. E60, 6172-6175.
    • (1999) Phys. Rev. , vol.E60 , pp. 6172-6175
    • Davidchack, R.L.1    Lai, Y.C.2
  • 21
    • 0001167045 scopus 로고    scopus 로고
    • Estimating generating partitions of chaotic systems by unstable periodic orbits
    • Davidchack, R. L., Lai, Y.-C., Bollt, E. M. & Dhamala, M. [2000] "Estimating generating partitions of chaotic systems by unstable periodic orbits," Phys. Rev. E61, 1353-1356.
    • (2000) Phys. Rev. , vol.E61 , pp. 1353-1356
    • Davidchack, R.L.1    Lai, Y.-C.2    Bollt, E.M.3    Dhamala, M.4
  • 22
    • 0035920641 scopus 로고    scopus 로고
    • Towards complete detection of unstable periodic orbits in chaotic systems
    • Davidchack, R. L., Lai, Y.-C., Klebanoff, A. & Bollt, E. M. [2001] "Towards complete detection of unstable periodic orbits in chaotic systems," Phys. Lett. A287, 99-104.
    • (2001) Phys. Lett. , vol.A287 , pp. 99-104
    • Davidchack, R.L.1    Lai, Y.-C.2    Klebanoff, A.3    Bollt, E.M.4
  • 23
    • 0000252317 scopus 로고
    • Obstructions to shadowing when a Lyapunov exponent fluctuates about zero
    • Dawson, S., Grebogi, C., Sauer, T. D. & Yorke, J. A. [1994] "Obstructions to shadowing when a Lyapunov exponent fluctuates about zero," Phys. Rev. Lett. 73, 1927-1930.
    • (1994) Phys. Rev. Lett. , vol.73 , pp. 1927-1930
    • Dawson, S.1    Grebogi, C.2    Sauer, T.D.3    Yorke, J.A.4
  • 24
    • 0034205556 scopus 로고    scopus 로고
    • Detecting unstable periodic orbits from transient chaotic time series
    • Dhamala, M., Lai, Y.-C. & Kostelich, E. J. [2000] "Detecting unstable periodic orbits from transient chaotic time series," Phys. Rev. E61, 6485-6489.
    • (2000) Phys. Rev. , vol.E61 , pp. 6485-6489
    • Dhamala, M.1    Lai, Y.-C.2    Kostelich, E.J.3
  • 25
    • 18144446486 scopus 로고    scopus 로고
    • Analysis of transient chaotic time series
    • Dhamala, M., Lai, Y.-C. & Kostelich, E. J. [2001] "Analysis of transient chaotic time series," Phys. Rev. E64, 056207(1-9).
    • (2001) Phys. Rev. , vol.E64 , pp. 0562071-0562079
    • Dhamala, M.1    Lai, Y.-C.2    Kostelich, E.J.3
  • 26
    • 0000822478 scopus 로고
    • Plateau onset for correlation dimension: When does it occur?
    • Ding, M., Grebogi, C., Ott, E., Sauer, T. D. & Yorke, J. A. [1993] "Plateau onset for correlation dimension: When does it occur?" Phys. Rev. Lett. 70, 3872-3875.
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 3872-3875
    • Ding, M.1    Grebogi, C.2    Ott, E.3    Sauer, T.D.4    Yorke, J.A.5
  • 27
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors
    • Eckmann, J.-P. & Ruelle, D. [1985] "Ergodic theory of chaos and strange attractors," Rev. Mod. Phys. 57, 617-656.
    • (1985) Rev. Mod. Phys. , vol.57 , pp. 617-656
    • Eckmann, J.-P.1    Ruelle, D.2
  • 29
    • 48749145669 scopus 로고
    • The dimension of chaotic attractors
    • Farmer, J. D., Ott, E. & Yorke, J. A. [1983] "The dimension of chaotic attractors," Physica D7, 153-180.
    • (1983) Physica , vol.D7 , pp. 153-180
    • Farmer, J.D.1    Ott, E.2    Yorke, J.A.3
  • 31
    • 0000293183 scopus 로고
    • Theory of communication
    • Gabor, D. [1946] "Theory of communication," J. IEE Lond. 93, 429-457.
    • (1946) J. IEE Lond. , vol.93 , pp. 429-457
    • Gabor, D.1
  • 33
    • 3342947955 scopus 로고    scopus 로고
    • Detecting functional relationships between simultaneous time series
    • Goodridge, C. L., Pecora, L. M., Carroll, T. L. & Rachford, F. J. [2001] "Detecting functional relationships between simultaneous time series," Phys. Rev. E64, 026221.
    • (2001) Phys. Rev. , vol.E64 , pp. 026221
    • Goodridge, C.L.1    Pecora, L.M.2    Carroll, T.L.3    Rachford, F.J.4
  • 34
    • 33646981873 scopus 로고
    • Characterization of strange attractors
    • Grassberger, P. & Procaccia, I. [1983a] "Characterization of strange attractors," Phys. Rev. Lett. 50, 346-348.
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 346-348
    • Grassberger, P.1    Procaccia, I.2
  • 35
    • 40749093037 scopus 로고
    • Measuring the strangeness of strange attractors
    • Grassberger, P. & Procaccia, I. [1983b] "Measuring the strangeness of strange attractors," Physica D9, 189-208.
    • (1983) Physica , vol.D9 , pp. 189-208
    • Grassberger, P.1    Procaccia, I.2
  • 36
    • 46549094713 scopus 로고
    • Repellers, semi-attractors, and long-lived chaotic transients
    • Grassberger, P. & Kantz, H. [1985] "Repellers, semi-attractors, and long-lived chaotic transients," Physica D17, 75-86.
    • (1985) Physica , vol.D17 , pp. 75-86
    • Grassberger, P.1    Kantz, H.2
  • 37
    • 5344274815 scopus 로고
    • Chaotic attractors in crisis
    • Grebogi, C., Ott, E. & Yorke, J. A. [1982] "Chaotic attractors in crisis," Phys. Rev. Lett 48, 1507-1510.
    • (1982) Phys. Rev. Lett , vol.48 , pp. 1507-1510
    • Grebogi, C.1    Ott, E.2    Yorke, J.A.3
  • 38
    • 0012349493 scopus 로고
    • Crises, sudden changes in chaotic attractors and chaotic transients
    • Grebogi, C., Ott, E. & Yorke, J. A. [1983] "Crises, sudden changes in chaotic attractors and chaotic transients," Physica D7, 181-200.
    • (1983) Physica , vol.D7 , pp. 181-200
    • Grebogi, C.1    Ott, E.2    Yorke, J.A.3
  • 39
    • 29444438680 scopus 로고
    • Unstable periodic orbits and the dimensions of multifractal chaotic attractors
    • Grebogi, C., Ott, E. & Yorke, J. A. [1988] "Unstable periodic orbits and the dimensions of multifractal chaotic attractors," Phys. Rev. A37, 1711-1724.
    • (1988) Phys. Rev. , vol.A37 , pp. 1711-1724
    • Grebogi, C.1    Ott, E.2    Yorke, J.A.3
  • 40
    • 0000263135 scopus 로고
    • Shadowing of physical trajectories in chaotic dynamics: Containment and refinement
    • Grebogi, C., Hammel, S. M., Yorke, J. A. & Sauer, T. D. [1990] "Shadowing of physical trajectories in chaotic dynamics: Containment and refinement," Phys. Rev. Lett. 65, 1527-1530.
    • (1990) Phys. Rev. Lett. , vol.65 , pp. 1527-1530
    • Grebogi, C.1    Hammel, S.M.2    Yorke, J.A.3    Sauer, T.D.4
  • 43
    • 45949120176 scopus 로고
    • Do numerical orbits of chaotic dynamical processes represent true orbits?
    • Hammel, S. M., Yorke, J. A. & Grebogi, C. [1987] "Do numerical orbits of chaotic dynamical processes represent true orbits?" J. Complexity 3, 136-145.
    • (1987) J. Complexity , vol.3 , pp. 136-145
    • Hammel, S.M.1    Yorke, J.A.2    Grebogi, C.3
  • 44
    • 84968480383 scopus 로고
    • Numerical orbits of chaotic processes represent true orbits
    • Hammel, S. M., Yorke, J. A. & Grebogi, C. [1988] "Numerical orbits of chaotic processes represent true orbits," Bull. Am. Math. Soc. 19, 465-469.
    • (1988) Bull. Am. Math. Soc. , vol.19 , pp. 465-469
    • Hammel, S.M.1    Yorke, J.A.2    Grebogi, C.3
  • 45
    • 0002591468 scopus 로고
    • A two-dimensional mapping with a strange attractor
    • Hénon, M. [1976] "A two-dimensional mapping with a strange attractor," Commun. Math. Phys. 50, 69-76.
    • (1976) Commun. Math. Phys. , vol.50 , pp. 69-76
    • Hénon, M.1
  • 46
    • 0000644990 scopus 로고
    • Strange saddles and the dimensions of their invariant manifolds
    • Hsu, G.-H., Ott, E. & Grebogi, C. [1988] "Strange saddles and the dimensions of their invariant manifolds," Phys. Lett. A127, 199-204.
    • (1988) Phys. Lett. , vol.A127 , pp. 199-204
    • Hsu, G.-H.1    Ott, E.2    Grebogi, C.3
  • 47
    • 5444236478 scopus 로고    scopus 로고
    • The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series
    • Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C. & Liu, H. H. [1998] "The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series," Proc. R. Soc. Land. A454, 903-995.
    • (1998) Proc. R. Soc. Land. , vol.A454 , pp. 903-995
    • Huang, N.E.1    Shen, Z.2    Long, S.R.3    Wu, M.C.4    Shih, H.H.5    Zheng, Q.6    Yen, N.C.7    Tung, C.C.8    Liu, H.H.9
  • 48
    • 0001600430 scopus 로고    scopus 로고
    • Fractal dimensions of chaotic saddles of dynamical systems
    • Hunt, B. R., Ott, E. & Yorke, J. A. [1996] "Fractal dimensions of chaotic saddles of dynamical systems," Phys. Rev. E54, 4819-4823.
    • (1996) Phys. Rev. , vol.E54 , pp. 4819-4823
    • Hunt, B.R.1    Ott, E.2    Yorke, J.A.3
  • 49
    • 0002427559 scopus 로고    scopus 로고
    • Computing the measure of nonattracting chaotic sets
    • Jacobs, J., Ott, E. & Grebogi, C. [1997] "Computing the measure of nonattracting chaotic sets," Physica D108, 1-11.
    • (1997) Physica , vol.D108 , pp. 1-11
    • Jacobs, J.1    Ott, E.2    Grebogi, C.3
  • 50
    • 0001085819 scopus 로고
    • Time-series analysis of transient chaos
    • Janosi, I. M. & Tél, T. [1994] "Time-series analysis of transient chaos," Phys. Rev. E49, 2756-2763.
    • (1994) Phys. Rev. , vol.E49 , pp. 2756-2763
    • Janosi, I.M.1    Tél, T.2
  • 51
    • 0000349274 scopus 로고
    • Chaotic advection in pulsed-source sink systems
    • Jones, S. W. & Aref, H. [1988] "Chaotic advection in pulsed-source sink systems," Phys. Fluids 31, 469-485.
    • (1988) Phys. Fluids , vol.31 , pp. 469-485
    • Jones, S.W.1    Aref, H.2
  • 52
    • 0024901211 scopus 로고
    • Chaotic advection by laminar-flow in a twisted pipe
    • Jones, S. W., Thomas, O. & Aref, H. [1989] "Chaotic advection by laminar-flow in a twisted pipe," J. Fluid. Mech. 209, 335-357.
    • (1989) J. Fluid. Mech. , vol.209 , pp. 335-357
    • Jones, S.W.1    Thomas, O.2    Aref, H.3
  • 53
    • 0000601315 scopus 로고
    • Hamiltonian scattering chaos in a hydrodynamical system
    • Jung, C. & Ziemniak, E. [1992] "Hamiltonian scattering chaos in a hydrodynamical system," J. Phys. A Math. Gen. 25, 3929-3943.
    • (1992) J. Phys. A Math. Gen. , vol.25 , pp. 3929-3943
    • Jung, C.1    Ziemniak, E.2
  • 54
    • 0001154059 scopus 로고
    • Application of scattering chaos to particle transport in hydrodynamical flow
    • Jung, C., Tél, T. & Ziemniak, E. [1993] "Application of scattering chaos to particle transport in hydrodynamical flow," Chaos 3, 555-568.
    • (1993) Chaos , vol.3 , pp. 555-568
    • Jung, C.1    Tél, T.2    Ziemniak, E.3
  • 56
    • 0031281070 scopus 로고    scopus 로고
    • Chaotic tracer scattering and fractal basin boundaries in a blinking vortex-sink system
    • Karolyi, G. & Tél, T. [1997] "Chaotic tracer scattering and fractal basin boundaries in a blinking vortex-sink system," Phys. Rep. 290, 125-147.
    • (1997) Phys. Rep. , vol.290 , pp. 125-147
    • Karolyi, G.1    Tél, T.2
  • 57
  • 58
    • 0002227785 scopus 로고
    • A correlation-function for choosing time delays in-phase portrait reconstructions
    • Kember, G. & Fowler, A. C. [1993] "A correlation-function for choosing time delays in-phase portrait reconstructions," Phys. Lett. A179, 72-80.
    • (1993) Phys. Lett. , vol.A179 , pp. 72-80
    • Kember, G.1    Fowler, A.C.2
  • 59
    • 0000906011 scopus 로고
    • How often are chaotic saddles nonhyperbolic?
    • Lai, Y.-C., Grebogi, C., Yorke, J. A. & Kan, I. [1993] "How often are chaotic saddles nonhyperbolic?" Nonlinearity 6, 779-797.
    • (1993) Nonlinearity , vol.6 , pp. 779-797
    • Lai, Y.-C.1    Grebogi, C.2    Yorke, J.A.3    Kan, I.4
  • 60
    • 0043016516 scopus 로고    scopus 로고
    • An upper bound for the proper delay time in chaotic time series analysis
    • Lai, Y.-C., Lerner, D. & Hayden, R. [1996] "An upper bound for the proper delay time in chaotic time series analysis," Phys. Lett. A218, 30-34.
    • (1996) Phys. Lett. , vol.A218 , pp. 30-34
    • Lai, Y.-C.1    Lerner, D.2    Hayden, R.3
  • 61
    • 0031332567 scopus 로고    scopus 로고
    • Characterization of the natural measure by unstable periodic orbits in nonhyperbolic chaotic systems
    • Lai, Y.-C. [1997] "Characterization of the natural measure by unstable periodic orbits in nonhyperbolic chaotic systems," Phys. Rev. 56, 6531-6539.
    • (1997) Phys. Rev. , vol.56 , pp. 6531-6539
    • Lai, Y.-C.1
  • 62
    • 0000861771 scopus 로고    scopus 로고
    • Characterization of the natural measure by unstable periodic orbits in chaotic attractors
    • Lai, Y.-C., Nagai, Y. & Grebogi, C. [1997] "Characterization of the natural measure by unstable periodic orbits in chaotic attractors," Phys. Rev. Lett. 79, 649-652.
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 649-652
    • Lai, Y.-C.1    Nagai, Y.2    Grebogi, C.3
  • 63
    • 0000021516 scopus 로고    scopus 로고
    • Analytic signals and the transition to chaos in deterministic flows
    • Lai, Y.-C. [1998] "Analytic signals and the transition to chaos in deterministic flows," Phys. Rev. E58, R6911-R6914.
    • (1998) Phys. Rev. , vol.E58
    • Lai, Y.-C.1
  • 64
    • 0002587376 scopus 로고    scopus 로고
    • Effective scaling regime for computing the correlation dimension in chaotic time series analysis
    • Lai, Y.-C. & Lerner, D. [1998] "Effective scaling regime for computing the correlation dimension in chaotic time series analysis," Physica D115, 1-18.
    • (1998) Physica , vol.D115 , pp. 1-18
    • Lai, Y.-C.1    Lerner, D.2
  • 65
    • 0032614845 scopus 로고    scopus 로고
    • Modeling of coupled chaotic oscillators
    • Lai, Y.-C. & Grebogi, C. [1999] "Modeling of coupled chaotic oscillators," Phys. Rev. Lett. 82, 4803-4806.
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 4803-4806
    • Lai, Y.-C.1    Grebogi, C.2
  • 66
    • 0033092741 scopus 로고    scopus 로고
    • Modeling of deterministic chaotic systems
    • Lai, Y.-C., Grebogi, C. & Kurths, J. [1999a] "Modeling of deterministic chaotic systems," Phys. Rev. E59, 2907-2910.
    • (1999) Phys. Rev. , vol.E59 , pp. 2907-2910
    • Lai, Y.-C.1    Grebogi, C.2    Kurths, J.3
  • 67
    • 0001460303 scopus 로고    scopus 로고
    • Unstable dimension variability in coupled chaotic oscillators
    • Lai, Y.-C., Lerner, D., Williams, K. & Grebogi, C. [1999b] "Unstable dimension variability in coupled chaotic oscillators," Phys. Rev. E60, 5445-5454.
    • (1999) Phys. Rev. , vol.E60 , pp. 5445-5454
    • Lai, Y.-C.1    Lerner, D.2    Williams, K.3    Grebogi, C.4
  • 68
    • 0002144874 scopus 로고
    • On the problem of turbulence
    • Landau, L. D. [1944] "On the problem of turbulence," C. R. Acad. Sci. USSR 44, 311-315.
    • (1944) C. R. Acad. Sci. USSR , vol.44 , pp. 311-315
    • Landau, L.D.1
  • 69
    • 4143093387 scopus 로고
    • Characterization of an experimental strange attractor by periodic orbits
    • Lathrop, D. P. & Kostelich, E. J. [1989] "Characterization of an experimental strange attractor by periodic orbits," Phys. Rev. A40, 4028-4031.
    • (1989) Phys. Rev. , vol.A40 , pp. 4028-4031
    • Lathrop, D.P.1    Kostelich, E.J.2
  • 70
    • 30244464950 scopus 로고
    • Proper choice of the time-delay for the analysis of chaotic time-series
    • Liebert, W. & Schuster, H. G. [1989] "Proper choice of the time-delay for the analysis of chaotic time-series," Phys. Lett. A142, 107-111.
    • (1989) Phys. Lett. , vol.A142 , pp. 107-111
    • Liebert, W.1    Schuster, H.G.2
  • 71
    • 84956258433 scopus 로고
    • Optimal embeddings of chaotic attractors from topological considerations
    • Liebert, W., Pawelzik, K. & Schuster, H. G. [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    Pawelzik, K.2    Schuster, H.G.3
  • 72
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • Lorenz, E. N. [1963] "Deterministic nonperiodic flow," J. Atmos. Sci. 20, 130-141.
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 75
    • 0000379341 scopus 로고    scopus 로고
    • Two-frequency motion to chaos with fractal dimension d > 3
    • Moon, H.-T. [1997] "Two-frequency motion to chaos with fractal dimension d > 3," Phys. Rev. Lett. 79, 403-406.
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 403-406
    • Moon, H.-T.1
  • 76
    • 0001240852 scopus 로고
    • On partial dimensions and spectra of singularities of strange attractors
    • Morita, T., Hata, H. Mori, H., Horita, T. & Tomita, K. [1987] "On partial dimensions and spectra of singularities of strange attractors," Prog. Theor. Phys. 78, 511-515.
    • (1987) Prog. Theor. Phys. , vol.78 , pp. 511-515
    • Morita, T.1    Hata, H.2    Mori, H.3    Horita, T.4    Tomita, K.5
  • 78
    • 37649031879 scopus 로고    scopus 로고
    • Finite-size effects on active chaotic advection
    • Nishikawa, T., Toroczkai, Z., Grebogi, C. & Tél, T. [2002] "Finite-size effects on active chaotic advection," Phys. Rev. E65, 026216.
    • (2002) Phys. Rev. , vol.E65 , pp. 026216
    • Nishikawa, T.1    Toroczkai, Z.2    Grebogi, C.3    Tél, T.4
  • 79
    • 45149143640 scopus 로고
    • A procedure for finding numerical trajectories on chaotic saddles
    • Nusse, H. E. & Yorke, J. A. [1989] "A procedure for finding numerical trajectories on chaotic saddles," Physica D36, 137-156.
    • (1989) Physica , vol.D36 , pp. 137-156
    • Nusse, H.E.1    Yorke, J.A.2
  • 82
    • 0003582543 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • Ott, E. [1993] Chaos in Dynamical Systems (Cambridge University Press, Cambridge, UK).
    • (1993) Chaos in Dynamical Systems
    • Ott, E.1
  • 84
    • 0001705102 scopus 로고
    • Unstable periodic orbits and prediction
    • Pawelzik, K. & Schuster, H. G. [1991] "Unstable periodic orbits and prediction," Phys. Rev. A43, 1808-1812.
    • (1991) Phys. Rev. , vol.A43 , pp. 1808-1812
    • Pawelzik, K.1    Schuster, H.G.2
  • 85
    • 0000686115 scopus 로고
    • Statistics for mathematical properties of maps between time series embeddings
    • Pecora, L. M., Carroll, T. L. & Heagy, J. F. [1995] "Statistics for mathematical properties of maps between time series embeddings," Phys. Rev. E52, 3420-3439.
    • (1995) Phys. Rev. , vol.E52 , pp. 3420-3439
    • Pecora, L.M.1    Carroll, T.L.2    Heagy, J.F.3
  • 86
    • 0012995124 scopus 로고    scopus 로고
    • Discontinuous and nondifferentiable functions and dimension increase induced by filtering chaotic data
    • Pecora, L. M. & Carroll, T. L. [1996] "Discontinuous and nondifferentiable functions and dimension increase induced by filtering chaotic data," Chaos 6, 432-439.
    • (1996) Chaos , vol.6 , pp. 432-439
    • Pecora, L.M.1    Carroll, T.L.2
  • 87
    • 0043213029 scopus 로고    scopus 로고
    • Statistics for continuity and differentiability: An application to attractor reconstruction from time series
    • Pecora, L. M., Carroll, T. L. & Heagy, J. F. [1997] "Statistics for continuity and differentiability: An application to attractor reconstruction from time series," Fields Inst. Commun. 11, 49-62.
    • (1997) Fields Inst. Commun. , vol.11 , pp. 49-62
    • Pecora, L.M.1    Carroll, T.L.2    Heagy, J.F.3
  • 88
    • 0040199887 scopus 로고    scopus 로고
    • Detecting chaotic drive-response geometry in generalized synchronization
    • Pecora, L. M. & Carroll, T. L. [2000] "Detecting chaotic drive-response geometry in generalized synchronization," Int. J. Bifurcation and Chaos 10, 875-889.
    • (2000) Int. J. Bifurcation and Chaos , vol.10 , pp. 875-889
    • Pecora, L.M.1    Carroll, T.L.2
  • 89
    • 0030052744 scopus 로고    scopus 로고
    • Characterization of low-dimensional dynamics in the crayfish caudal photoreceptor
    • Pei, X. & Moss, F. [1996a] "Characterization of low-dimensional dynamics in the crayfish caudal photoreceptor," Nature 379, 618-621.
    • (1996) Nature , vol.379 , pp. 618-621
    • Pei, X.1    Moss, F.2
  • 90
    • 0030228982 scopus 로고    scopus 로고
    • Detecting low dimensional dynamics in biological experiments
    • Pei, X. & Moss, F. [1996b] "Detecting low dimensional dynamics in biological experiments," Int. J. Neural Syst. 7, 429-435.
    • (1996) Int. J. Neural Syst. , vol.7 , pp. 429-435
    • Pei, X.1    Moss, F.2
  • 91
    • 0000390258 scopus 로고    scopus 로고
    • Counting unstable periodic orbits in noisy chaotic systems: A scaling relation connecting experiment with theory
    • Pei, X., Dolan, K., Moss, F. & Lai, Y.-C. [1998] "Counting unstable periodic orbits in noisy chaotic systems: A scaling relation connecting experiment with theory," Chaos 8, 853-860.
    • (1998) Chaos , vol.8 , pp. 853-860
    • Pei, X.1    Dolan, K.2    Moss, F.3    Lai, Y.-C.4
  • 92
    • 0001587809 scopus 로고
    • Fractal boundaries in open hydrodynamical flows: Signatures of chaotic saddles
    • Péntek, A., Toroczkai, Z., Tél, T., Grebogi, C. & Yorke, J. A. [1995] "Fractal boundaries in open hydrodynamical flows: Signatures of chaotic saddles," Phys. Rev. E51, 4076-4088.
    • (1995) Phys. Rev. , vol.E51 , pp. 4076-4088
    • Péntek, A.1    Toroczkai, Z.2    Tél, T.3    Grebogi, C.4    Yorke, J.A.5
  • 93
    • 0000576711 scopus 로고
    • Detecting periodic unstable points in noisy chaotic and limit-cycle attractors with applications to biology
    • Pierson, D. & Moss, F. [1995] "Detecting periodic unstable points in noisy chaotic and limit-cycle attractors with applications to biology," Phys. Rev. Lett. 75, 2124-2127.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 2124-2127
    • Pierson, D.1    Moss, F.2
  • 94
    • 0035419825 scopus 로고    scopus 로고
    • Detecting unstable periodic orbits in chaotic continuous-time dynamical systems
    • Pingel, D., Schmelcher, P. & Diakonos, F. K. [2001] "Detecting unstable periodic orbits in chaotic continuous-time dynamical systems," Phys. Rev. E64, 026214.
    • (2001) Phys. Rev. , vol.E64 , pp. 026214
    • Pingel, D.1    Schmelcher, P.2    Diakonos, F.K.3
  • 96
    • 4243262725 scopus 로고    scopus 로고
    • Phase synchronization of chaotic oscillators
    • Rosenblum, M. G., Pikovsky, A. S. & Kurths, J. [1996] "Phase synchronization of chaotic oscillators," Phys. Rev. Lett. 76, 1804-1807.
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 1804-1807
    • Rosenblum, M.G.1    Pikovsky, A.S.2    Kurths, J.3
  • 97
    • 26544461279 scopus 로고
    • Reconstruction expansion as a geometry-based framework for choosing proper delay times
    • Rosenstein, M. T., Collins, J. J. & De Luca, C. J. [1994] "Reconstruction expansion as a geometry-based framework for choosing proper delay times," Physica D73, 82-98.
    • (1994) Physica , vol.D73 , pp. 82-98
    • Rosenstein, M.T.1    Collins, J.J.2    De Luca, C.J.3
  • 98
    • 49549126801 scopus 로고
    • Equation for continuous chaos
    • Rössler, O. E. [1976] "Equation for continuous chaos," Phys. Lett. A57, 397-398.
    • (1976) Phys. Lett. , vol.A57 , pp. 397-398
    • Rössler, O.E.1
  • 100
    • 0001394076 scopus 로고
    • Measurement of the Lyapunov spectrum from a chaotic time series
    • Sano, M. & Sawada, Y. [1985] "Measurement of the Lyapunov spectrum from a chaotic time series," Phys. Rev. Lett. 55, 1082-1085.
    • (1985) Phys. Rev. Lett. , vol.55 , pp. 1082-1085
    • Sano, M.1    Sawada, Y.2
  • 102
    • 0001470336 scopus 로고    scopus 로고
    • Spurious Lyapunov exponents in attractor reconstruction
    • Sauer, T. D., Tempkin, J. A. & Yorke, J. A. [1998] "Spurious Lyapunov exponents in attractor reconstruction," Phys. Rev. Lett. 81, 4341-4344.
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 4341-4344
    • Sauer, T.D.1    Tempkin, J.A.2    Yorke, J.A.3
  • 103
    • 0001248042 scopus 로고    scopus 로고
    • Reconstructing the Jacobian from data with observational noise
    • Sauer, T. D. & Yorke, J. A. [1999] "Reconstructing the Jacobian from data with observational noise," Phys. Rev. Lett. 83, 1331-1334.
    • (1999) Phys. Rev. Lett. , vol.83 , pp. 1331-1334
    • Sauer, T.D.1    Yorke, J.A.2
  • 105
    • 6144249748 scopus 로고    scopus 로고
    • Detecting unstable periodic orbits of chaotic dynamical systems
    • Schmelcher, P. & Diakonos, F. K. [1997] "Detecting unstable periodic orbits of chaotic dynamical systems," Phys. Rev. Lett. 78, 4733-4736.
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 4733-4736
    • Schmelcher, P.1    Diakonos, F.K.2
  • 106
    • 0032025560 scopus 로고    scopus 로고
    • General approach to the localization of unstable periodic orbits in chaotic dynamical systems
    • Schmelcher, P. & Diakonos, F. K. [1998] "General approach to the localization of unstable periodic orbits in chaotic dynamical systems, " Phys. Rev. E57, 2739-2746.
    • (1998) Phys. Rev. , vol.E57 , pp. 2739-2746
    • Schmelcher, P.1    Diakonos, F.K.2
  • 107
    • 0001550469 scopus 로고    scopus 로고
    • Systematic computation of the least unstable periodic orbits in chaotic attractors
    • Schmelcher, P., Diakonos, F. K. & Biham, O. [1998] "Systematic computation of the least unstable periodic orbits in chaotic attractors," Phys. Rev. Lett. 81, 4349-4352.
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 4349-4352
    • Schmelcher, P.1    Diakonos, F.K.2    Biham, O.3
  • 109
    • 84968514104 scopus 로고
    • Didifferentiable dynamics systems
    • Smale, S. [1967] "Didifferentiable dynamics systems," Bull. Amer. Math. Soc. 73, 747-817.
    • (1967) Bull. Amer. Math. Soc. , vol.73 , pp. 747-817
    • Smale, S.1
  • 111
    • 4243769823 scopus 로고    scopus 로고
    • Extracting unstable periodic orbits from chaotic time series data
    • So, P., Ott, E., Sauer, T. D., Gluckman, B. J., Grebogi, C. & Schiff, S. J. [1997] "Extracting unstable periodic orbits from chaotic time series data," Phys. Rev. E55, 5398-5417.
    • (1997) Phys. Rev. , vol.E55 , pp. 5398-5417
    • So, P.1    Ott, E.2    Sauer, T.D.3    Gluckman, B.J.4    Grebogi, C.5    Schiff, S.J.6
  • 112
    • 21844527214 scopus 로고
    • A simple model of chaotic advection and scattering
    • Stolovitzky, G., Kaper, T. J. & Sirovich, L. [1995] "A simple model of chaotic advection and scattering," Chaos 5, 671-686.
    • (1995) Chaos , vol.5 , pp. 671-686
    • Stolovitzky, G.1    Kaper, T.J.2    Sirovich, L.3
  • 113
    • 0000779360 scopus 로고
    • Detecting strange attractors in fluid turbulence
    • eds. Rand, D. & Young, L. S. (Springer-Verlag, Berlin)
    • Takens, F. [1981] "Detecting strange attractors in fluid turbulence," Dynamical Systems and Turbulence (Lecture Notes in Mathematics), eds. Rand, D. & Young, L. S. (Springer-Verlag, Berlin), pp. 366-381.
    • (1981) Dynamical Systems and Turbulence (Lecture Notes in Mathematics) , pp. 366-381
    • Takens, F.1
  • 115
    • 85038170840 scopus 로고
    • Focus issues on chaotic scattering
    • Tél, T. & Ott, E. [1993] "Focus issues on chaotic scattering," Chaos 3, 417-706.
    • (1993) Chaos , vol.3 , pp. 417-706
    • Tél, T.1    Ott, E.2
  • 116
    • 0000613208 scopus 로고    scopus 로고
    • Transient chaos: A type of metastable state
    • ed. Hao, B.-L. (World Scientific, Singapore)
    • Tél, T. [1996] "Transient chaos: A type of metastable state," STATPHYS 19: The Proc. 19th IUPAP Conf. Statistical Physics, ed. Hao, B.-L. (World Scientific, Singapore), pp. 346-362.
    • (1996) STATPHYS 19: The Proc. 19th IUPAP Conf. Statistical Physics , pp. 346-362
    • Tél, T.1
  • 117
    • 0001413326 scopus 로고
    • Spurious dimension from correlation algorithms applied to limited time series data
    • Theiler, J. [1986] "Spurious dimension from correlation algorithms applied to limited time series data," Phys. Rev. A34, 2427-2432.
    • (1986) Phys. Rev. , vol.A34 , pp. 2427-2432
    • Theiler, J.1
  • 119
    • 0008494528 scopus 로고
    • Determining Lyapunov exponents from a time series
    • Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. [1985] "Determining Lyapunov exponents from a time series," Physica D16, 285-317.
    • (1985) Physica , vol.D16 , pp. 285-317
    • Wolf, A.1    Swift, J.B.2    Swinney, H.L.3    Vastano, J.A.4
  • 120
    • 0001216578 scopus 로고    scopus 로고
    • Phase characterization of chaos
    • Yalcinkaya, T. & Lai, Y.-C. [1997] "Phase characterization of chaos," Phys. Rev. Lett. 79, 3787-3790.
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 3787-3790
    • Yalcinkaya, T.1    Lai, Y.-C.2
  • 122
    • 36449005018 scopus 로고
    • Shear dispersion
    • Young, W. R. & Jones, S. W. [1991] "Shear dispersion," Phys. Fluids A3, 1087-1101.
    • (1991) Phys. Fluids , vol.A3 , pp. 1087-1101
    • Young, W.R.1    Jones, S.W.2
  • 123
    • 43949161715 scopus 로고
    • Tracer dynamics in open hydrodynamical flows as chaotic scattering
    • Ziemniak, E., Jung, C. & Tél, T. [1994] "Tracer dynamics in open hydrodynamical flows as chaotic scattering," Physica D76, 123-146.
    • (1994) Physica , vol.D76 , pp. 123-146
    • Ziemniak, E.1    Jung, C.2    Tél, T.3
  • 124
    • 0032028875 scopus 로고    scopus 로고
    • Spatially localized unstable periodic orbits of a high-dimensional chaotic system
    • Zoldi, S. M. & Greenside, H. S. [1998] "Spatially localized unstable periodic orbits of a high-dimensional chaotic system," Phys. Rev. E57, R2511-R2514.
    • (1998) Phys. Rev. , vol.E57
    • Zoldi, S.M.1    Greenside, H.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.