-
2
-
-
12044249591
-
The analysis of observed chaotic data in physical systems
-
H.D.I. Abarbanel, R. Brown, J.J. Sidorowich, L.Sh. Tsimring, The analysis of observed chaotic data in physical systems, Rev. Mod. Phys. 65 (1993) 1331.
-
(1993)
Rev. Mod. Phys.
, vol.65
, pp. 1331
-
-
Abarbanel, H.D.I.1
Brown, R.2
Sidorowich, J.J.3
Tsimring, L.Sh.4
-
3
-
-
0000062618
-
Chaotic time series I, Modeling
-
D. Kugiumtzis, B. Lillekjendlie, N. Christophersen, Chaotic time series I, Modeling, Identification Control 15 (1994) 205.
-
(1994)
Identification Control
, vol.15
, pp. 205
-
-
Kugiumtzis, D.1
Lillekjendlie, B.2
Christophersen, N.3
-
4
-
-
0000230666
-
Chaotic Time Series II, Modeling
-
D. Kugiumtzis, B. Lillekjendlie, N. Christophersen, Chaotic Time Series II, Modeling, Identification Control 15 (1994) 225.
-
(1994)
Identification Control
, vol.15
, pp. 225
-
-
Kugiumtzis, D.1
Lillekjendlie, B.2
Christophersen, N.3
-
5
-
-
0003861548
-
-
Wiley, New York
-
E. Ott, T. Sauer, J.A. Yorke, Coping with Chaos, Wiley, New York, 1994.
-
(1994)
Coping with Chaos
-
-
Ott, E.1
Sauer, T.2
Yorke, J.A.3
-
9
-
-
0038993594
-
Nonlinear modeling and forecasting
-
Addison-Wesley, Reading, MA
-
M. Casdagli, S. Eubank (Eds.), Nonlinear modeling and forecasting, Santa Fe Institute Studies in the Science of Complexity, Proc. Vol. XII, Addison-Wesley, Reading, MA, 1992.
-
(1992)
Santa Fe Institute Studies in the Science of Complexity, Proc.
, vol.12
-
-
Casdagli, M.1
Eubank, S.2
-
10
-
-
0003251836
-
Time series prediction: Forecasting the future and understanding the past
-
Addison-Wesley, Reading, MA
-
A.S. Weigend, N.A. Gershenfeld (Eds.), Time series prediction: forecasting the future and understanding the past, Santa Fe Institute Studies in the Science of Complexity, Proc. Vol. XV, Addison-Wesley, Reading, MA, 1993.
-
(1993)
Santa Fe Institute Studies in the Science of Complexity, Proc.
, vol.15
-
-
Weigend, A.S.1
Gershenfeld, N.A.2
-
11
-
-
0003820053
-
-
AIP Press, New York
-
J. Bélair, L. Glass, U. an der Heiden, J. Milton (Eds.), Dynamical Disease, AIP Press, New York, 1995.
-
(1995)
Dynamical Disease
-
-
Bélair, J.1
Glass, L.2
An Der Heiden, U.3
Milton, J.4
-
12
-
-
0347875170
-
-
Springer Series in Synergetics, Springer, Heidelberg
-
H. Kantz, J. Kurths, G. Mayer-Kress (Eds.), Nonlinear Techniques in Physiological Time Series Analysis, Springer Series in Synergetics, Springer, Heidelberg, 1998.
-
(1998)
Nonlinear Techniques in Physiological Time Series Analysis
-
-
Kantz, H.1
Kurths, J.2
Mayer-Kress, G.3
-
15
-
-
0001499851
-
Is there a climatic attractor?
-
C. Nicolis, G. Nicolis, Is there a climatic attractor?, Nature 326 (1987) 523.
-
(1987)
Nature
, vol.326
, pp. 523
-
-
Nicolis, C.1
Nicolis, G.2
-
16
-
-
0001267036
-
Estimating the dimensions of weather and climate attractors
-
K. Fraedrich, Estimating the dimensions of weather and climate attractors, J. Atmos. Sci. 43 (1986) 419.
-
(1986)
J. Atmos. Sci.
, vol.43
, pp. 419
-
-
Fraedrich, K.1
-
17
-
-
0023486115
-
The climate attractor over short time scales
-
C. Essex, T. Lockman, M.A.H. Nerenberg, The climate attractor over short time scales, Nature 326 (1987) 64.
-
(1987)
Nature
, vol.326
, pp. 64
-
-
Essex, C.1
Lockman, T.2
Nerenberg, M.A.H.3
-
18
-
-
84977719043
-
Chaos and nonlinear dynamics: Applications to financial markets
-
D.A. Hsieh, Chaos and nonlinear dynamics: applications to financial markets, J. Finance 46 (1991) 1839.
-
(1991)
J. Finance
, vol.46
, pp. 1839
-
-
Hsieh, D.A.1
-
19
-
-
0001949095
-
A chaotic attractor for the s + p 500
-
E.E. Peters, A chaotic attractor for the s + p 500, Financial Analysts J. 3 (1991) 55.
-
(1991)
Financial Analysts J.
, vol.3
, pp. 55
-
-
Peters, E.E.1
-
21
-
-
0024207280
-
Nonlinear dynamics in sudden cardiac death syndrome: Heart rate oscillations and bifurcations
-
A.L. Goldberger, D.R. Rigney, J. Mietus, E.M. Antman, S. Greenwald, Nonlinear dynamics in sudden cardiac death syndrome: heart rate oscillations and bifurcations, Experientia 44 (1988) 983.
-
(1988)
Experientia
, vol.44
, pp. 983
-
-
Goldberger, A.L.1
Rigney, D.R.2
Mietus, J.3
Antman, E.M.4
Greenwald, S.5
-
22
-
-
0023546965
-
Non-linear dynamics in cardiac excitation and impulse propagation
-
D.R. Chialvo, J. Jalife, Non-linear dynamics in cardiac excitation and impulse propagation, Nature 330 (1987) 749.
-
(1987)
Nature
, vol.330
, pp. 749
-
-
Chialvo, D.R.1
Jalife, J.2
-
23
-
-
0042723063
-
Strange attractors in the dynamics of brain activity
-
H. Haken (Ed.), Springer, Berlin
-
A. Babloyantz, Strange attractors in the dynamics of brain activity, in: H. Haken (Ed.), Complex Systems, Springer, Berlin, 1985.
-
(1985)
Complex Systems
-
-
Babloyantz, A.1
-
24
-
-
0025820018
-
Electroencephalographic effects of cigarette smoking
-
W.S. Pritchard, Electroencephalographic effects of cigarette smoking, Psychopharmacology 104 (1991) 485.
-
(1991)
Psychopharmacology
, vol.104
, pp. 485
-
-
Pritchard, W.S.1
-
26
-
-
0003582543
-
-
Cambridge University Press, Cambridge
-
E. Ott, Chaos in Dynamical Systems, Cambridge University Press, Cambridge, 1993.
-
(1993)
Chaos in Dynamical Systems
-
-
Ott, E.1
-
27
-
-
0003683539
-
-
Wiley, New York
-
P. Bergé, Y. Pomeau, C. Vidal, Order Within Chaos: Towards a Deterministic Approach to Turbulence, Wiley, New York, 1986.
-
(1986)
Order Within Chaos: Towards a Deterministic Approach to Turbulence
-
-
Bergé, P.1
Pomeau, Y.2
Vidal, C.3
-
32
-
-
0000303832
-
Noise in chaotic data: Diagnosis and treatment
-
Reprinted in [11]
-
T. Schreiber, H. Kantz, Noise in chaotic data: Diagnosis and treatment, CHAOS 5 (1995) 133; Reprinted in [11].
-
(1995)
Chaos
, vol.5
, pp. 133
-
-
Schreiber, T.1
Kantz, H.2
-
33
-
-
0001637554
-
Effective deterministic models for chaotic dynamics perturbed by noise
-
L. Jaeger, H. Kantz, Effective deterministic models for chaotic dynamics perturbed by noise, Phys. Rev. E 55 (1997) 5234.
-
(1997)
Phys. Rev. E
, vol.55
, pp. 5234
-
-
Jaeger, L.1
Kantz, H.2
-
34
-
-
34249982739
-
Predicting chaotic time series
-
Reprinted in [5]
-
J.D. Farmer, J. Sidorowich, Predicting chaotic time series, Phys. Rev. Lett. 59 (1987) 845; Reprinted in [5].
-
(1987)
Phys. Rev. Lett.
, vol.59
, pp. 845
-
-
Farmer, J.D.1
Sidorowich, J.2
-
35
-
-
45149144372
-
Nonlinear prediction of chaotic time series
-
Reprinted in [5]
-
M. Casdagli, Nonlinear prediction of chaotic time series, Physica D 35 (1989) 335; Reprinted in [5].
-
(1989)
Physica D
, vol.35
, pp. 335
-
-
Casdagli, M.1
-
36
-
-
0001341233
-
Problems in estimating dynamics from data
-
E.J. Kostelich, Problems in estimating dynamics from data, Physica D 58 (1992) 138.
-
(1992)
Physica D
, vol.58
, pp. 138
-
-
Kostelich, E.J.1
-
37
-
-
0001128249
-
Unbiased reconstruction underlying a noisy chaotic time series
-
L. Jaeger, H. Kantz, Unbiased reconstruction underlying a noisy chaotic time series, CHAOS 6 (1996) 440.
-
(1996)
Chaos
, vol.6
, pp. 440
-
-
Jaeger, L.1
Kantz, H.2
-
38
-
-
0001581120
-
Modeling and synchronizing chaotic systems from time-series data
-
R. Brown, E.R. Rulkov, N.F. Tracy, Modeling and synchronizing chaotic systems from time-series data, Phys. Rev. E 49 (1994) 3784.
-
(1994)
Phys. Rev. E
, vol.49
, pp. 3784
-
-
Brown, R.1
Rulkov, E.R.2
Tracy, N.F.3
-
39
-
-
0000779360
-
Detecting strange attractors in turbulence
-
D.A. Rand, L.-S. Young (Eds.), Dynamical Systems and Turbulence, Springer, New York
-
F. Takens, Detecting strange attractors in turbulence, in: D.A. Rand, L.-S. Young (Eds.), Dynamical Systems and Turbulence, Lecture Notes in Mathematics, vol. 898, Springer, New York, 1981.
-
(1981)
Lecture Notes in Mathematics
, vol.898
-
-
Takens, F.1
-
41
-
-
0041375087
-
Takens embedding theorems for forced and stochastic systems
-
J. Stark, D.S. Broomhead, M.E. Davies, J. Huke, Takens embedding theorems for forced and stochastic systems, Nonlinear Analysis 30 (1997) 5303.
-
(1997)
Nonlinear Analysis
, vol.30
, pp. 5303
-
-
Stark, J.1
Broomhead, D.S.2
Davies, M.E.3
Huke, J.4
-
42
-
-
21344485017
-
How many delay coordinates do you need?
-
T. Sauer, J. Yorke, How many delay coordinates do you need?, Int. J. Bifurcation Chaos 3 (1993) 737.
-
(1993)
Int. J. Bifurcation Chaos
, vol.3
, pp. 737
-
-
Sauer, T.1
Yorke, J.2
-
43
-
-
0004161838
-
-
Cambridge University Press, Cambridge
-
W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes, 2nd ed., Cambridge University Press, Cambridge, 1992.
-
(1992)
Numerical Recipes, 2nd Ed.
-
-
Press, W.H.1
Flannery, B.P.2
Teukolsky, S.A.3
Vetterling, W.T.4
-
44
-
-
43949166788
-
A practical method for calculating largest Lyapunov exponents from small data sets
-
M.T. Rosenstein, J.J. Collins, C.J. De Luca, A practical method for calculating largest Lyapunov exponents from small data sets, Physica D 65 (1993) 117.
-
(1993)
Physica D
, vol.65
, pp. 117
-
-
Rosenstein, M.T.1
Collins, J.J.2
De Luca, C.J.3
-
45
-
-
0001870258
-
A robust method to estimate the maximal Lyapunov exponent of a time series
-
H. Kantz, A robust method to estimate the maximal Lyapunov exponent of a time series, Phys. Lett. A 185 (1994) 77.
-
(1994)
Phys. Lett. A
, vol.185
, pp. 77
-
-
Kantz, H.1
-
46
-
-
6444240297
-
Lyapunov exponents from a time series
-
Reprinted in [5]
-
J.-P. Eckmann, S. Oliffson Kamphorst, D. Ruelle, S. Ciliberto, Lyapunov exponents from a time series, Phys. Rev. A 34 (1986) 4971; Reprinted in [5].
-
(1986)
Phys. Rev. A
, vol.34
, pp. 4971
-
-
Eckmann, J.-P.1
Oliffson Kamphorst, S.2
Ruelle, D.3
Ciliberto, S.4
-
47
-
-
0001394076
-
Measurement of the Lyapunov spectrum from a chaotic time series
-
M. Sano, Y. Sawada, Measurement of the Lyapunov spectrum from a chaotic time series, Phys. Rev. Lett. 55 (1985) 1082.
-
(1985)
Phys. Rev. Lett.
, vol.55
, pp. 1082
-
-
Sano, M.1
Sawada, Y.2
-
48
-
-
0001036423
-
Evaluation of Lyapunov exponents and scaling functions from time series
-
R. Stoop, P.F. Meier, Evaluation of Lyapunov exponents and scaling functions from time series, J. Opt. Soc. Am. B 5 (1988) 1037.
-
(1988)
J. Opt. Soc. Am. B
, vol.5
, pp. 1037
-
-
Stoop, R.1
Meier, P.F.2
-
49
-
-
0005875463
-
Calculation of Lyapunov exponents avoiding spurious elements
-
R. Stoop, J. Parisi, Calculation of Lyapunov exponents avoiding spurious elements, Physica D 50 (1991) 89.
-
(1991)
Physica D
, vol.50
, pp. 89
-
-
Stoop, R.1
Parisi, J.2
-
51
-
-
0000974708
-
Local optimal prediction: Exploiting strangeness and the variation of sensitiy to initial condition
-
L.A. Smith, Local optimal prediction: exploiting strangeness and the variation of sensitiy to initial condition, Philos. Trans. Roy. Soc. A 348 (1994) 371.
-
(1994)
Philos. Trans. Roy. Soc. A
, vol.348
, pp. 371
-
-
Smith, L.A.1
-
53
-
-
33750490125
-
Local Lyapunov exponents in chaotic systems
-
B. Eckhardt, D. Yao, Local Lyapunov exponents in chaotic systems, Physica D 65 (1993) 100.
-
(1993)
Physica D
, vol.65
, pp. 100
-
-
Eckhardt, B.1
Yao, D.2
-
54
-
-
0002986576
-
Chaos with confidence: Asymptotics and applications of local Lyapunov exponents
-
B.A. Bailey, S. Ellner, D.W. Nychka, Chaos with confidence: asymptotics and applications of local Lyapunov exponents, Fields Inst. Comm. 11 (1997) 115.
-
(1997)
Fields Inst. Comm.
, vol.11
, pp. 115
-
-
Bailey, B.A.1
Ellner, S.2
Nychka, D.W.3
-
55
-
-
40749093037
-
Measuring the strangeness of strange attractors
-
P. Grassberger, I. Procaccia, Measuring the strangeness of strange attractors, Physica D 9 (1983) 189.
-
(1983)
Physica D
, vol.9
, pp. 189
-
-
Grassberger, P.1
Procaccia, I.2
-
56
-
-
0000945887
-
2-entropy calculations by means of dimension scaled distances
-
2-entropy calculations by means of dimension scaled distances, Physica D 65 (1993) 359.
-
(1993)
Physica D
, vol.65
, pp. 359
-
-
Frank, M.1
Blank, H.-R.2
Heindl, J.3
Kaltenhäuser, M.4
Köchner, H.5
Müller, N.6
Pocher, S.7
Sporer, R.8
Wagner, T.9
-
57
-
-
0013309515
-
Assessing different norms in nonlinear analysis of noisy time series
-
D. Kugiumtzis, Assessing different norms in nonlinear analysis of noisy time series, Physica D 105 (1997) 62.
-
(1997)
Physica D
, vol.105
, pp. 62
-
-
Kugiumtzis, D.1
-
58
-
-
0001450027
-
Generalized redundancies for time series analysis
-
D. Prichard, J. Theiler, Generalized redundancies for time series analysis, Physica D 84 (1995) 476.
-
(1995)
Physica D
, vol.84
, pp. 476
-
-
Prichard, D.1
Theiler, J.2
-
59
-
-
0000842022
-
Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems
-
A. Cohen, I. Procaccia, Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems, Phys. Rev. A 31 (1985) 1872.
-
(1985)
Phys. Rev. A
, vol.31
, pp. 1872
-
-
Cohen, A.1
Procaccia, I.2
-
60
-
-
0000401256
-
Integrated wavelets on fractal sets I: The correlation dimension
-
J.M. Ghez, S. Vaienti, Integrated wavelets on fractal sets I: the correlation dimension, Nonlinearity 5 (1992) 777.
-
(1992)
Nonlinearity
, vol.5
, pp. 777
-
-
Ghez, J.M.1
Vaienti, S.2
-
61
-
-
2342578642
-
Integrated wavelets on fractal sets II: The generalized dimensions
-
J.M. Ghez, S. Vaienti, Integrated wavelets on fractal sets II: the generalized dimensions, Nonlinearity 5 (1992) 791.
-
(1992)
Nonlinearity
, vol.5
, pp. 791
-
-
Ghez, J.M.1
Vaienti, S.2
-
62
-
-
0028928878
-
Measuring the dissimilarity between EEG recordings through a non-linear dynamical system approach
-
J.L. Hernández, R. Biscay, J.C. Jimenez, P. Valdes, R. Grave de Peralta, Measuring the dissimilarity between EEG recordings through a non-linear dynamical system approach, Int. J. Bio-Med. Comp. 38 (1995) 121.
-
(1995)
Int. J. Bio-Med. Comp.
, vol.38
, pp. 121
-
-
Hernández, J.L.1
Biscay, R.2
Jimenez, J.C.3
Valdes, P.4
De Grave Peralta, R.5
-
63
-
-
0000484363
-
Classification of time series data with nonlinear similarity measures
-
T. Schreiber, A. Schmitz, Classification of time series data with nonlinear similarity measures, Phys. Rev. Lett. 79 (1997) 1475.
-
(1997)
Phys. Rev. Lett.
, vol.79
, pp. 1475
-
-
Schreiber, T.1
Schmitz, A.2
-
64
-
-
22244479670
-
Stationarity and nonstationarity in time series analysis
-
R. Manuca, R. Savit, Stationarity and nonstationarity in time series analysis, Physica D 99 (1996) 134.
-
(1996)
Physica D
, vol.99
, pp. 134
-
-
Manuca, R.1
Savit, R.2
-
65
-
-
18744431041
-
Non-linearity in invasive EEG recordings from patients with temporal lobe epilepsy
-
M.C. Casdagli, L.D. Iasemidis, R.S. Savit, R.L. Gilmore, S. Roper, J.C. Sackellares, Non-linearity in invasive EEG recordings from patients with temporal lobe epilepsy, Electroencephalogr. Clin. Neurophysiol. 102 (1997) 98.
-
(1997)
Electroencephalogr. Clin. Neurophysiol.
, vol.102
, pp. 98
-
-
Casdagli, M.C.1
Iasemidis, L.D.2
Savit, R.S.3
Gilmore, R.L.4
Roper, S.5
Sackellares, J.C.6
-
66
-
-
0000828959
-
Detecting and analysing nonstationarity in a time series using nonlinear cross predictions
-
T. Schreiber, Detecting and analysing nonstationarity in a time series using nonlinear cross predictions, Phys. Rev. Lett. 78 (1997) 843.
-
(1997)
Phys. Rev. Lett.
, vol.78
, pp. 843
-
-
Schreiber, T.1
-
67
-
-
0000686115
-
Statistics for mathematical properties of maps between time series embeddings
-
L.M. Pecora, T.L. Carroll, J.F. Heagy, Statistics for mathematical properties of maps between time series embeddings, Phys. Rev. E 52 (1995) 3420.
-
(1995)
Phys. Rev. E
, vol.52
, pp. 3420
-
-
Pecora, L.M.1
Carroll, T.L.2
Heagy, J.F.3
-
68
-
-
11944272386
-
General approach for chaotic synchronization with applications to communication
-
L. Kocarev, U. Parlitz, General approach for chaotic synchronization with applications to communication, Phys. Rev. Lett. 74 (1995) 5028.
-
(1995)
Phys. Rev. Lett.
, vol.74
, pp. 5028
-
-
Kocarev, L.1
Parlitz, U.2
-
69
-
-
0000929946
-
Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems
-
L. Kocarev, U. Parlitz, Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems, Phys. Rev. Lett. 76 (1996) 1816.
-
(1996)
Phys. Rev. Lett.
, vol.76
, pp. 1816
-
-
Kocarev, L.1
Parlitz, U.2
-
70
-
-
33744833457
-
Generalized synchronization of chaos in directionally coupled chaotic systems
-
N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, H.D.I. Abarbanel, Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E 51 (1995) 980.
-
(1995)
Phys. Rev. E
, vol.51
, pp. 980
-
-
Rulkov, N.F.1
Sushchik, M.M.2
Tsimring, L.S.3
Abarbanel, H.D.I.4
-
73
-
-
0001209622
-
Quantifying the closeness of factal measures
-
H. Kantz, Quantifying the closeness of factal measures, Phys. Rev. E 49 (1994) 5091.
-
(1994)
Phys. Rev. E
, vol.49
, pp. 5091
-
-
Kantz, H.1
-
74
-
-
0001541230
-
Detecting differences between delay vector distributions
-
C. Diks, W.R. van Zwet, F. Takens, J. DeGoede, Detecting differences between delay vector distributions, Phys. Rev. E 53 (1996) 2169.
-
(1996)
Phys. Rev. E
, vol.53
, pp. 2169
-
-
Diks, C.1
Van Zwet, W.R.2
Takens, F.3
DeGoede, J.4
-
75
-
-
0000225025
-
Measuring the distance between time series
-
R. Moeckel, B. Murray, Measuring the distance between time series, Physica D 102 (1997) 187.
-
(1997)
Physica D
, vol.102
, pp. 187
-
-
Moeckel, R.1
Murray, B.2
-
76
-
-
36348931715
-
Classification of highly noisy signals using global dynamical models
-
J. Kadtke, Classification of highly noisy signals using global dynamical models, Phys. Lett. A 203 (1995) 196.
-
(1995)
Phys. Lett. A
, vol.203
, pp. 196
-
-
Kadtke, J.1
-
77
-
-
44949273552
-
State space reconstruction in the presence of noise
-
M. Casdagli, S. Eubank, J.D. Farmer, J. Gibson, State space reconstruction in the presence of noise, Physica D 51 (1991) 52.
-
(1991)
Physica D
, vol.51
, pp. 52
-
-
Casdagli, M.1
Eubank, S.2
Farmer, J.D.3
Gibson, J.4
-
79
-
-
0032094997
-
Delay embedding in the presence of dynamical noise
-
M.R. Muldoon, D.S. Broomhead, J.P. Huke, R. Hegger, Delay embedding in the presence of dynamical noise, Dyn. Stab. Systems 13 (1998) 175.
-
(1998)
Dyn. Stab. Systems
, vol.13
, pp. 175
-
-
Muldoon, M.R.1
Broomhead, D.S.2
Huke, J.P.3
Hegger, R.4
-
80
-
-
0000822478
-
Plateau onset for correlation dimension: When does it occur?
-
Reprinted in [5]
-
M. Ding, C. Grebogi, E. Ott, T. Sauer, J.A. Yorke, Plateau onset for correlation dimension: When does it occur? Phys. Rev. Lett. 70 (1993) 3872; Reprinted in [5].
-
(1993)
Phys. Rev. Lett.
, vol.70
, pp. 3872
-
-
Ding, M.1
Grebogi, C.2
Ott, E.3
Sauer, T.4
Yorke, J.A.5
-
81
-
-
0039106963
-
Limitations of delay reconstruction for chaotic systems with a broad spectrum
-
G.G. Malinetskii, A.B. Potapov, A.I. Rakhmanov, E.B. Rodichev, Limitations of delay reconstruction for chaotic systems with a broad spectrum, Phys. Lett. A 179 (1993) 15.
-
(1993)
Phys. Lett. A
, vol.179
, pp. 15
-
-
Malinetskii, G.G.1
Potapov, A.B.2
Rakhmanov, A.I.3
Rodichev, E.B.4
-
82
-
-
34548696055
-
Independent coordinates for strange attractors from mutual information
-
A.M. Fraser, H.L. Swinney, Independent coordinates for strange attractors from mutual information, Phys. Rev. A 33 (1986) 1134.
-
(1986)
Phys. Rev. A
, vol.33
, pp. 1134
-
-
Fraser, A.M.1
Swinney, H.L.2
-
83
-
-
30244464950
-
Proper choice of the time delays for the analysis of chaotic time series
-
W. Liebert, H.G. Schuster, Proper choice of the time delays for the analysis of chaotic time series, Phys. Lett. A 142 (1989) 107.
-
(1989)
Phys. Lett. A
, vol.142
, pp. 107
-
-
Liebert, W.1
Schuster, H.G.2
-
84
-
-
84956258433
-
Optimal embeddings of chaotic attractors from topological considerations
-
W. Liebert, K. Pawelzik, H.G. Schuster, Optimal embeddings of chaotic attractors from topological considerations, Europhys. Lett. 14 (1991) 521.
-
(1991)
Europhys. Lett.
, vol.14
, pp. 521
-
-
Liebert, W.1
Pawelzik, K.2
Schuster, H.G.3
-
85
-
-
0001282028
-
Method to distinguish possible chaos from colored noise and to determine embedding parameters
-
M.B. Kennel, S. Isabelle, Method to distinguish possible chaos from colored noise and to determine embedding parameters, Phys. Rev. A 46 (1992) 3111.
-
(1992)
Phys. Rev. A
, vol.46
, pp. 3111
-
-
Kennel, M.B.1
Isabelle, S.2
-
86
-
-
44049113708
-
Comparison of algorithms calculating optimal parameters for delay time coordinates
-
T. Buzug, G. Pfister, Comparison of algorithms calculating optimal parameters for delay time coordinates, Physica D 58 (1992) 127.
-
(1992)
Physica D
, vol.58
, pp. 127
-
-
Buzug, T.1
Pfister, G.2
-
87
-
-
84956277039
-
Optimal reconstruction of strange attractors from purely geometrical arguments
-
T. Buzug, T. Reimers, G. Pfister, Optimal reconstruction of strange attractors from purely geometrical arguments, Europhys. Lett. 13 (1990) 605.
-
(1990)
Europhys. Lett.
, vol.13
, pp. 605
-
-
Buzug, T.1
Reimers, T.2
Pfister, G.3
-
88
-
-
0002624834
-
State space reconstruction parameters in the analysis of chaotic time series - The role of the time window length
-
D. Kugiumtzis, State space reconstruction parameters in the analysis of chaotic time series - the role of the time window length, Physica D 95 (1996) 13.
-
(1996)
Physica D
, vol.95
, pp. 13
-
-
Kugiumtzis, D.1
-
89
-
-
0001981585
-
Observing and predicting chaotic signals: Is 2% noise too much?
-
Y. Kravtsov, J. Kadtke (Eds.), Springer, New York
-
T. Schreiber, H. Kantz, Observing and predicting chaotic signals: is 2% noise too much? in: Y. Kravtsov, J. Kadtke (Eds.), Predictability of Complex Dynamical Systems, Springer, New York, 1996.
-
(1996)
Predictability of Complex Dynamical Systems
-
-
Schreiber, T.1
Kantz, H.2
-
92
-
-
0000202504
-
Chaos and deterministic versus stochastic nonlinear modeling
-
M. Casdagli, Chaos and deterministic versus stochastic nonlinear modeling, J. Roy. Stat. Soc. 54 (1991) 303.
-
(1991)
J. Roy. Stat. Soc.
, vol.54
, pp. 303
-
-
Casdagli, M.1
-
93
-
-
0014534148
-
Atmospheric predictability as revealed by naturally occurring analogues
-
E.N. Lorenz, Atmospheric predictability as revealed by naturally occurring analogues, J. Atmos. Sci. 26 (1969) 636.
-
(1969)
J. Atmos. Sci.
, vol.26
, pp. 636
-
-
Lorenz, E.N.1
-
95
-
-
0025199496
-
Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series
-
Reprinted in [5]
-
G. Sugihara, R. May, Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series, Nature 344 (1990) 734; Reprinted in [5].
-
(1990)
Nature
, vol.344
, pp. 734
-
-
Sugihara, G.1
May, R.2
-
96
-
-
34250112778
-
On the concept of attractor
-
J. Milnor, On the concept of attractor, Comm. Math. Phys. 99 (1985) 177.
-
(1985)
Comm. Math. Phys.
, vol.99
, pp. 177
-
-
Milnor, J.1
-
97
-
-
0002432565
-
Multivariate adaptive regression splines
-
J.H. Friedman, Multivariate adaptive regression splines (with discussion), Ann. Stat. 19 (1991) 1.
-
(1991)
Ann. Stat.
, vol.19
, pp. 1
-
-
Friedman, J.H.1
-
99
-
-
0000621802
-
Multivariable function interpolation and adaptive networks
-
D. Broomhead, D. Lowe, Multivariable function interpolation and adaptive networks, Complex Syst. 2 (1988) 321.
-
(1988)
Complex Syst.
, vol.2
, pp. 321
-
-
Broomhead, D.1
Lowe, D.2
-
100
-
-
0001977937
-
Identification and prediction of low-dimensional dynamics
-
L.A. Smith, Identification and prediction of low-dimensional dynamics, Physica D 58 (1992) 50.
-
(1992)
Physica D
, vol.58
, pp. 50
-
-
Smith, L.A.1
-
101
-
-
0003802343
-
-
Chapman & Hall, New York
-
L. Breiman, J.H. Friedman, R.A. Olshen, C.J. Stone, Classification and Regression Trees, Chapman & Hall, New York, 1993.
-
(1993)
Classification and Regression Trees
-
-
Breiman, L.1
Friedman, J.H.2
Olshen, R.A.3
Stone, C.J.4
-
102
-
-
0016355478
-
A new look at the statistical model identification
-
H. Akaike, A new look at the statistical model identification, IEEE Trans. Automat. Control AC-19 (1974) 716.
-
(1974)
IEEE Trans. Automat. Control
, vol.AC-19
, pp. 716
-
-
Akaike, H.1
-
103
-
-
0003093019
-
Consistent order estimates of autoregressive processes by shortest description of data
-
O. Jacobs et al. (Eds.), Academic Press, New York
-
J. Rissanen, Consistent order estimates of autoregressive processes by shortest description of data, in: O. Jacobs et al. (Eds.), Analysis and Optimisation of Stochastic Systems, Academic Press, New York, 1980.
-
(1980)
Analysis and Optimisation of Stochastic Systems
-
-
Rissanen, J.1
-
104
-
-
0001959743
-
Using 'Surrogate Surrogate Data' to calibrate the actual rate of false positives in tests for nonlinearity in time series
-
J. Theiler, D. Prichard, Using 'Surrogate Surrogate Data' to calibrate the actual rate of false positives in tests for nonlinearity in time series, Fields Inst. Comm. 11 (1997) 99.
-
(1997)
Fields Inst. Comm.
, vol.11
, pp. 99
-
-
Theiler, J.1
Prichard, D.2
-
105
-
-
0008494528
-
Determining Lyapunov exponents from a time series
-
A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Determining Lyapunov exponents from a time series, Physica D 16 (1985) 285.
-
(1985)
Physica D
, vol.16
, pp. 285
-
-
Wolf, A.1
Swift, J.B.2
Swinney, H.L.3
Vastano, J.A.4
-
106
-
-
0000471425
-
Comparison of different methods for computing Lyapunov exponents
-
K. Geist, U. Parlitz, W. Lauterborn, Comparison of different methods for computing Lyapunov exponents, Prog. Thoeor. Phys. 83 (1990) 875.
-
(1990)
Prog. Thoeor. Phys.
, vol.83
, pp. 875
-
-
Geist, K.1
Parlitz, U.2
Lauterborn, W.3
-
107
-
-
0000478578
-
Statistical precision of dimension estimators
-
J. Theiler, Statistical precision of dimension estimators, Phys. Rev. A 41 (1990) 3038.
-
(1990)
Phys. Rev. A
, vol.41
, pp. 3038
-
-
Theiler, J.1
-
108
-
-
0004576571
-
Estimating dimension in noisy chaotic time-series
-
R.L. Smith, Estimating dimension in noisy chaotic time-series, J.R. Statist. Soc. B 54 (1992) 329.
-
(1992)
J.R. Statist. Soc. B
, vol.54
, pp. 329
-
-
Smith, R.L.1
-
109
-
-
0002405786
-
On the numerical determination of the dimension of an attractor
-
B.L.J. Braaksma, H.W. Broer, F. Takens (Eds.), Dynamical systems and bifurcations, Springer, Heidelberg
-
F. Takens, On the numerical determination of the dimension of an attractor, in: B.L.J. Braaksma, H.W. Broer, F. Takens (Eds.), Dynamical systems and bifurcations, Lecture Notes in Mathematics, vol. 1125, Springer, Heidelberg, 1985.
-
(1985)
Lecture Notes in Mathematics
, vol.1125
-
-
Takens, F.1
-
110
-
-
0001743732
-
Some results on the behavior and estimation of the fractal dimensions of distributions on attractors
-
C.D. Cutler, Some results on the behavior and estimation of the fractal dimensions of distributions on attractors, J. Stat. Phys. 62 (1991) 651.
-
(1991)
J. Stat. Phys.
, vol.62
, pp. 651
-
-
Cutler, C.D.1
-
111
-
-
0006314948
-
A theory of correlation dimension for stationary time series
-
C.D. Cutler, A theory of correlation dimension for stationary time series, Philosoph. Trans. Royal Soc. London A 348 (1995) 343.
-
(1995)
Philosoph. Trans. Royal Soc. London A
, vol.348
, pp. 343
-
-
Cutler, C.D.1
-
112
-
-
5544310124
-
Finite correlation dimension for stochastic systems with power-law spectra
-
A.R. Osborne, A. Provenzale, Finite correlation dimension for stochastic systems with power-law spectra, Physica D 35 (1989) 357.
-
(1989)
Physica D
, vol.35
, pp. 357
-
-
Osborne, A.R.1
Provenzale, A.2
-
114
-
-
0022855557
-
Do climatic attractors exist?
-
P. Grassberger, Do climatic attractors exist? Nature 323 (1986) 609.
-
(1986)
Nature
, vol.323
, pp. 609
-
-
Grassberger, P.1
-
115
-
-
0006275088
-
Evidence or climatic attractors: Grassberger replies
-
P. Grassberger, Evidence or climatic attractors: Grassberger replies, Nature 326 (1987) 524.
-
(1987)
Nature
, vol.326
, pp. 524
-
-
Grassberger, P.1
-
116
-
-
0001285133
-
Deterministic chaos: The science and the fiction
-
D. Ruelle, Deterministic chaos: the science and the fiction, Proc. R. Soc. London A 427 (1990) 241.
-
(1990)
Proc. R. Soc. London A
, vol.427
, pp. 241
-
-
Ruelle, D.1
-
117
-
-
84975613293
-
Estimating fractal dimension
-
J. Theiler, Estimating fractal dimension, J. Opt. Soc. Amer. A 7 (1990) 1055.
-
(1990)
J. Opt. Soc. Amer. A
, vol.7
, pp. 1055
-
-
Theiler, J.1
-
118
-
-
0001554852
-
Dimension estimates and physiological data
-
Reprinted in [11]
-
H. Kantz, T. Schreiber, Dimension estimates and physiological data, CHAOS 5 (1995) 143; Reprinted in [11].
-
(1995)
CHAOS
, vol.5
, pp. 143
-
-
Kantz, H.1
Schreiber, T.2
-
119
-
-
0000090102
-
Finite sample corrections to entropy and dimension estimates
-
P. Grassberger, Finite sample corrections to entropy and dimension estimates, Phys. Lett. A 128 (1988) 369.
-
(1988)
Phys. Lett. A
, vol.128
, pp. 369
-
-
Grassberger, P.1
-
120
-
-
44049112233
-
Distinguishing between low-dimensional dynamics and randomness in measured time series
-
A. Provenzale, L.A. Smith, R. Vio, G. Murante, Distinguishing between low-dimensional dynamics and randomness in measured time series, Physica D 58 (1992) 31.
-
(1992)
Physica D
, vol.58
, pp. 31
-
-
Provenzale, A.1
Smith, L.A.2
Vio, R.3
Murante, G.4
-
121
-
-
35949006791
-
Determining embedding dimension for phase-space reconstruction using a geometrical construction
-
Reprinted in [5]
-
M.B. Kennel, R. Brown, H.D.I. Abarbanel, Determining embedding dimension for phase-space reconstruction using a geometrical construction, Phys. Rev. A 45 (1992) 3403; Reprinted in [5].
-
(1992)
Phys. Rev. A
, vol.45
, pp. 3403
-
-
Kennel, M.B.1
Brown, R.2
Abarbanel, H.D.I.3
-
123
-
-
0000419983
-
Lacunarity in a best estimator of fractal dimension
-
J. Theiler, Lacunarity in a best estimator of fractal dimension, Phys. Lett. A 135 (1988) 195.
-
(1988)
Phys. Lett. A
, vol.135
, pp. 195
-
-
Theiler, J.1
-
124
-
-
0000954285
-
Estimating invariants of noisy attractors
-
C. Diks, Estimating invariants of noisy attractors, Phys. Rev. E 53 (1996) 4263.
-
(1996)
Phys. Rev. E
, vol.53
, pp. 4263
-
-
Diks, C.1
-
125
-
-
0004599587
-
Correction of the correlation dimension for noisy time series
-
D. Kugiumtzis, Correction of the correlation dimension for noisy time series, Int. J. Bifurcation Chaos 7 (1997) 1283.
-
(1997)
Int. J. Bifurcation Chaos
, vol.7
, pp. 1283
-
-
Kugiumtzis, D.1
-
126
-
-
0000124043
-
The influence of noise on power law scaling functions and an algorithm for dimension estimations
-
H. Oltmans, P.J.T. Verheijen, The influence of noise on power law scaling functions and an algorithm for dimension estimations, Phys. Rev. E 56 (1997) 1160.
-
(1997)
Phys. Rev. E
, vol.56
, pp. 1160
-
-
Oltmans, H.1
Verheijen, P.J.T.2
-
127
-
-
34147178673
-
Determination of the noise level of chaotic time series
-
T. Schreiber, Determination of the noise level of chaotic time series, Phys. Rev. E 48 (1993) 13.
-
(1993)
Phys. Rev. E
, vol.48
, pp. 13
-
-
Schreiber, T.1
-
128
-
-
0004544772
-
Influence of Gaussian noise on the correlation exponent
-
T. Schreiber, Influence of Gaussian noise on the correlation exponent, Phys. Rev. E 56 (1997) 274.
-
(1997)
Phys. Rev. E
, vol.56
, pp. 274
-
-
Schreiber, T.1
-
129
-
-
0011198007
-
A maximum likelihood approach to correlation dimension and entropy estimation
-
E. Olofsen, J. Degoede, R. Heijungs, A maximum likelihood approach to correlation dimension and entropy estimation, Bull. Math. Biol. 54 (1992) 45.
-
(1992)
Bull. Math. Biol.
, vol.54
, pp. 45
-
-
Olofsen, E.1
Degoede, J.2
Heijungs, R.3
-
130
-
-
18444400763
-
Maximum likelihood estimation of the entropy of an attractor
-
J.C. Schouten, F. Takens, C.M. van den Bleek, Maximum likelihood estimation of the entropy of an attractor, Phys. Rev. E 49 (1994) 126.
-
(1994)
Phys. Rev. E
, vol.49
, pp. 126
-
-
Schouten, J.C.1
Takens, F.2
Van Den Bleek, C.M.3
-
131
-
-
0031843242
-
Seizure prediction by nonlinear time series analysis of brain electrical activity
-
C. Elger, K. Lehnertz, Seizure prediction by nonlinear time series analysis of brain electrical activity, European J. Neuroscience 10 (1998) 786.
-
(1998)
European J. Neuroscience
, vol.10
, pp. 786
-
-
Elger, C.1
Lehnertz, K.2
-
132
-
-
0000058449
-
Symbolic dynamics for hyperbolic flows
-
R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973) 429.
-
(1973)
Amer. J. Math.
, vol.95
, pp. 429
-
-
Bowen, R.1
-
133
-
-
0343040265
-
Symbolic encoding in symplectic maps
-
F. Christiansen, A. Politi, Symbolic encoding in symplectic maps, Nonlinearity 9 (1996) 1623.
-
(1996)
Nonlinearity
, vol.9
, pp. 1623
-
-
Christiansen, F.1
Politi, A.2
-
134
-
-
0039659690
-
Generating partitions for the dissipative Hénon map
-
P. Grassberger, H. Kantz, Generating partitions for the dissipative Hénon map, Phys. Lett. A 113 (1985) 235.
-
(1985)
Phys. Lett. A
, vol.113
, pp. 235
-
-
Grassberger, P.1
Kantz, H.2
-
135
-
-
0000561572
-
Compelxity of symbol sequences
-
H. Herzel, Compelxity of symbol sequences, Syst. Anal. Modl. Simul. 5 (1988) 435.
-
(1988)
Syst. Anal. Modl. Simul.
, vol.5
, pp. 435
-
-
Herzel, H.1
-
136
-
-
0002993626
-
Entropy, transinformation and word distribution of information-carrying sequences
-
W. Ebeling, Th. Pöschel, K.-F. Albrecht, Entropy, transinformation and word distribution of information-carrying sequences, Int. J. Bifurcation Chaos 5 (1995) 51.
-
(1995)
Int. J. Bifurcation Chaos
, vol.5
, pp. 51
-
-
Ebeling, W.1
Pöschel, Th.2
Albrecht, K.-F.3
-
137
-
-
0040973114
-
Entropy estimation of symbol sequences
-
T. Schürmann, P. Grassberger, Entropy estimation of symbol sequences, CHAOS 6 (1996) 414.
-
(1996)
Chaos
, vol.6
, pp. 414
-
-
Schürmann, T.1
Grassberger, P.2
-
139
-
-
0028261351
-
A comparative classification of complexity measures
-
R. Wackerbauer, A. Witt, H. Atmanspacher, J. Kurths, H. Scheingraber, A comparative classification of complexity measures, Chaos Solitons Fractals 4 (1994) 133.
-
(1994)
Chaos Solitons Fractals
, vol.4
, pp. 133
-
-
Wackerbauer, R.1
Witt, A.2
Atmanspacher, H.3
Kurths, J.4
Scheingraber, H.5
-
140
-
-
0003031097
-
Complexity measures for the analysis of heart rate variability
-
J. Kurths, A. Voss, P. Saparin, A. Witt, H.J. Kleiner, N. Wessel, Complexity measures for the analysis of heart rate variability, CHAOS 5 (1995) 88.
-
(1995)
Chaos
, vol.5
, pp. 88
-
-
Kurths, J.1
Voss, A.2
Saparin, P.3
Witt, A.4
Kleiner, H.J.5
Wessel, N.6
-
141
-
-
0003621624
-
-
University of Wisconsin Press, Madison
-
W.A. Brock, W.D. Dechert, J.A. Scheinkman, B. LeBaron, A Test for Independence Based on the Correlation Dimension, University of Wisconsin Press, Madison, 1988.
-
(1988)
A Test for Independence Based on the Correlation Dimension
-
-
Brock, W.A.1
Dechert, W.D.2
Scheinkman, J.A.3
LeBaron, B.4
-
142
-
-
0003566244
-
-
MIT Press, Cambridge, MA
-
W.A. Brock, D.A. Hseih, B. LeBaron, Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence, MIT Press, Cambridge, MA, 1991.
-
(1991)
Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence
-
-
Brock, W.A.1
Hseih, D.A.2
LeBaron, B.3
-
144
-
-
0000510147
-
Detection of nonlinear dynamics in short, noisy time series
-
M. Barahona, C.-S. Poon, Detection of nonlinear dynamics in short, noisy time series, Nature 381 (1996) 215.
-
(1996)
Nature
, vol.381
, pp. 215
-
-
Barahona, M.1
Poon, C.-S.2
-
145
-
-
0000541993
-
Discrimination power of measures for nonlinearity in a time series
-
T. Schreiber, A. Schmitz, Discrimination power of measures for nonlinearity in a time series, Phys. Rev. E 55 (1997) 5443.
-
(1997)
Phys. Rev. E
, vol.55
, pp. 5443
-
-
Schreiber, T.1
Schmitz, A.2
-
146
-
-
11944266815
-
Direct test for determinism in a time series
-
Reprinted in [5]
-
D.T. Kaplan, L. Glass, Direct test for determinism in a time series, Phys. Rev. Lett. 68 (1992) 427; Reprinted in [5].
-
(1992)
Phys. Rev. Lett.
, vol.68
, pp. 427
-
-
Kaplan, D.T.1
Glass, L.2
-
147
-
-
0003207190
-
Measuring statistical dependencies in a time series
-
B. Pompe, Measuring statistical dependencies in a time series, J. Stat. Phys. 73 (1993) 587.
-
(1993)
J. Stat. Phys.
, vol.73
, pp. 587
-
-
Pompe, B.1
-
148
-
-
4243440738
-
Testing for nonlinearity using redundancies: Quantitative and qualitative aspects
-
M. Paluš, Testing for nonlinearity using redundancies: Quantitative and qualitative aspects, Physica D 80 (1995) 186.
-
(1995)
Physica D
, vol.80
, pp. 186
-
-
Paluš, M.1
-
149
-
-
0011079452
-
On entropy rates of dynamical systems and Gaussian processes
-
M. Paluš, On entropy rates of dynamical systems and Gaussian processes, Phys. Lett. A 227 (1997) 301.
-
(1997)
Phys. Lett. A
, vol.227
, pp. 301
-
-
Paluš, M.1
-
150
-
-
0000965724
-
Exploring chaotic motion through periodic orbits
-
D. Auerbach, P. Cvitanović, J.-P. Eckmann, G. Gunaratne, I. Procaccia, Exploring chaotic motion through periodic orbits, Phys. Rev. Lett. 58 (1987) 2387.
-
(1987)
Phys. Rev. Lett.
, vol.58
, pp. 2387
-
-
Auerbach, D.1
Cvitanović, P.2
Eckmann, J.-P.3
Gunaratne, G.4
Procaccia, I.5
-
154
-
-
12044250364
-
Progress in the analysis of experimental chaos through periodic orbits
-
R. Badii, E. Brun, M. Finardi, L. Flepp, R. Holzner, J. Parisi, C. Reyl, J. Simonet, Progress in the analysis of experimental chaos through periodic orbits, Rev. Mod. Phys. 66 (1994) 1389.
-
(1994)
Rev. Mod. Phys.
, vol.66
, pp. 1389
-
-
Badii, R.1
Brun, E.2
Finardi, M.3
Flepp, L.4
Holzner, R.5
Parisi, J.6
Reyl, C.7
Simonet, J.8
-
155
-
-
0001024141
-
Classification of strange attractors by integers
-
G.B. Mindlin, X.-J. Hou, H.G. Solari, R. Gilmore, N.B. Tufillaro, Classification of strange attractors by integers, Phys. Rev. Lett. 64 (1990) 2350.
-
(1990)
Phys. Rev. Lett.
, vol.64
, pp. 2350
-
-
Mindlin, G.B.1
Hou, X.-J.2
Solari, H.G.3
Gilmore, R.4
Tufillaro, N.B.5
-
157
-
-
0000576711
-
Detecting periodic unstable points in noisy chaotic and limit cycle attractors with applications to biology
-
D. Pierson, F. Moss, Detecting periodic unstable points in noisy chaotic and limit cycle attractors with applications to biology, Phys. Rev. Lett. 75 (1995) 2124.
-
(1995)
Phys. Rev. Lett.
, vol.75
, pp. 2124
-
-
Pierson, D.1
Moss, F.2
-
158
-
-
0001066377
-
Detecting unstable periodic orbits in chaotic experimental data
-
P. So, E. Ott, S.J. Schiff, D.T. Kaplan, T. Sauer, C. Grebogi, Detecting unstable periodic orbits in chaotic experimental data, Phys. Rev. Lett. 76 (1996) 4705.
-
(1996)
Phys. Rev. Lett.
, vol.76
, pp. 4705
-
-
So, P.1
Ott, E.2
Schiff, S.J.3
Kaplan, D.T.4
Sauer, T.5
Grebogi, C.6
-
159
-
-
0000152926
-
Controlling nonchaotic neuronal noise using chaos control techniques
-
D.J. Christini, J.J. Collins, Controlling nonchaotic neuronal noise using chaos control techniques, Phys. Rev. Lett. 75 (1995) 2782.
-
(1995)
Phys. Rev. Lett.
, vol.75
, pp. 2782
-
-
Christini, D.J.1
Collins, J.J.2
-
160
-
-
0001612833
-
Kolmogorov-Smirnov test distinguishes attractors with similar dimensions
-
A.M. Albano, P.E. Rapp, A. Passamante, Kolmogorov-Smirnov test distinguishes attractors with similar dimensions, Phys. Rev. E 52 (1995) 196.
-
(1995)
Phys. Rev. E
, vol.52
, pp. 196
-
-
Albano, A.M.1
Rapp, P.E.2
Passamante, A.3
-
161
-
-
21344494067
-
A test for stationarity: Finding parts in a time series apt for correlation dimension estimates
-
H. Isliker, J. Kurths, A test for stationarity: finding parts in a time series apt for correlation dimension estimates, Int. J. Bifurcation Chaos 3 (1993) 1573.
-
(1993)
Int. J. Bifurcation Chaos
, vol.3
, pp. 1573
-
-
Isliker, H.1
Kurths, J.2
-
162
-
-
0001562120
-
Statistical test for dynamical nonstationarity in observed time-series data
-
M.B. Kennel, Statistical test for dynamical nonstationarity in observed time-series data, Phys. Rev. E 56 (1997) 316.
-
(1997)
Phys. Rev. E
, vol.56
, pp. 316
-
-
Kennel, M.B.1
-
165
-
-
0002434633
-
Recurrence matrices and the preservation of dynamical properties
-
G. McGuire, N.B. Azar, M. Shelhamer, Recurrence matrices and the preservation of dynamical properties, Phys. Lett. A 237 (1997) 43.
-
(1997)
Phys. Lett. A
, vol.237
, pp. 43
-
-
McGuire, G.1
Azar, N.B.2
Shelhamer, M.3
-
166
-
-
0028354598
-
Dynamical assessment of physiological systems and states using recurrence plot strategies
-
C.L. Webber, J.P. Zbilut, Dynamical assessment of physiological systems and states using recurrence plot strategies, J. Appl. Physiol. 76 (1994) 965.
-
(1994)
J. Appl. Physiol.
, vol.76
, pp. 965
-
-
Webber, C.L.1
Zbilut, J.P.2
-
167
-
-
0042357254
-
Recurrence quantification analysis and principal components in the detection of short complex signals
-
J.P. Zbilut, A. Giuliani, C.L. Webber, Recurrence quantification analysis and principal components in the detection of short complex signals, Phys. Lett. A 237 (1998) 131.
-
(1998)
Phys. Lett. A
, vol.237
, pp. 131
-
-
Zbilut, J.P.1
Giuliani, A.2
Webber, C.L.3
-
168
-
-
22244460535
-
Recurrence plots revisited
-
M. Casdagli, Recurrence plots revisited, Physica D 108 (1997) 206.
-
(1997)
Physica D
, vol.108
, pp. 206
-
-
Casdagli, M.1
-
170
-
-
0001249676
-
Chaotic time series analyses of epileptic seizures
-
G.W. Frank, T. Lookman, M.A.H. Nerenberg, C. Essex, J. Lemieux, W. Blume, Chaotic time series analyses of epileptic seizures, Physica D 46 (1990) 427.
-
(1990)
Physica D
, vol.46
, pp. 427
-
-
Frank, G.W.1
Lookman, T.2
Nerenberg, M.A.H.3
Essex, C.4
Lemieux, J.5
Blume, W.6
-
171
-
-
43949156836
-
On the evidence for low-dimensional chaos in an epileptic electroencephalogram
-
J. Theiler, On the evidence for low-dimensional chaos in an epileptic electroencephalogram, Phys. Lett. A 196 (1995) 335.
-
(1995)
Phys. Lett. A
, vol.196
, pp. 335
-
-
Theiler, J.1
-
172
-
-
0029925526
-
Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram
-
J. Theiler, P.E. Rapp, Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram, Electroencephalogr. Clin. Neurophysiol. 98 (1996) 213.
-
(1996)
Electroencephalogr. Clin. Neurophysiol.
, vol.98
, pp. 213
-
-
Theiler, J.1
Rapp, P.E.2
-
173
-
-
22244454103
-
Monitoring changing dynamics with correlation integrals: Case study of an epileptic seizure
-
D.E. Lerner, Monitoring changing dynamics with correlation integrals: case study of an epileptic seizure, Physica D 97 (1996) 563.
-
(1996)
Physica D
, vol.97
, pp. 563
-
-
Lerner, D.E.1
-
174
-
-
0025950341
-
Chaos or noise in EEG signals; dependence on state and brain site
-
J.P. Pijn, J. Van Neerven, A. Noest, F.H. Lopes da Silva, Chaos or noise in EEG signals; dependence on state and brain site, Electroencephalogr. Clin. Neurophysiol. 79 (1991) 371.
-
(1991)
Electroencephalogr. Clin. Neurophysiol.
, vol.79
, pp. 371
-
-
Pijn, J.P.1
Van Neerven, J.2
Noest, A.3
Lopes Da Silva, F.H.4
-
175
-
-
0029123213
-
Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss
-
K. Lehnertz, C.E. Elger, Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss, Electroencephalogr. Clin. Neurophysiol. 95 (1995) 108.
-
(1995)
Electroencephalogr. Clin. Neurophysiol.
, vol.95
, pp. 108
-
-
Lehnertz, K.1
Elger, C.E.2
-
176
-
-
4243516693
-
Entropy quantification of human brain spatio-temporal dynamics
-
L. Pézard, J. Martinerie, J. Müller-Gerking, F.J. Varela, B. Renault, Entropy quantification of human brain spatio-temporal dynamics, Physica D 96 (1996) 344.
-
(1996)
Physica D
, vol.96
, pp. 344
-
-
Pézard, L.1
Martinerie, J.2
Müller-Gerking, J.3
Varela, F.J.4
Renault, B.5
-
178
-
-
44949291358
-
Takens versus multichannel reconstruction in EEG correlation exponent estimates
-
I. Dvorak, Takens versus multichannel reconstruction in EEG correlation exponent estimates, Phys. Lett. A 151 (1990) 225.
-
(1990)
Phys. Lett. A
, vol.151
, pp. 225
-
-
Dvorak, I.1
-
179
-
-
0000702943
-
Correlation dimension of intermittent signals
-
R. Hegger, H. Kantz, E. Olbrich, Correlation dimension of intermittent signals, Phys. Rev. E 56 (1997) 199.
-
(1997)
Phys. Rev. E
, vol.56
, pp. 199
-
-
Hegger, R.1
Kantz, H.2
Olbrich, E.3
-
180
-
-
44049111332
-
Testing for nonlinearity in time series: The method of surrogate data
-
Reprinted in [5]
-
J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, J.D. Farmer, Testing for nonlinearity in time series: the method of surrogate data Physica D 58 (1992) 77; Reprinted in [5].
-
(1992)
Physica D
, vol.58
, pp. 77
-
-
Theiler, J.1
Eubank, S.2
Longtin, A.3
Galdrikian, B.4
Farmer, J.D.5
-
181
-
-
0000314757
-
-
in [9]
-
J. Theiler, B. Galdrikian, A. Longtin, S. Eubank, J.D. Farmer, Using surrogate data to detect nonlinearity in time series, in [9].
-
Using Surrogate Data to Detect Nonlinearity in Time Series
-
-
Theiler, J.1
Galdrikian, B.2
Longtin, A.3
Eubank, S.4
Farmer, J.D.5
-
182
-
-
0003299258
-
An Introduction to Bispectral Analysis and Bilinear Time Series Models
-
Springer, New York
-
T. Subba Rao, M.M. Gabr, An Introduction to Bispectral Analysis and Bilinear Time Series Models, Lecture Notes in Statistics, vol. 24, Springer, New York, 1984.
-
(1984)
Lecture Notes in Statistics
, vol.24
-
-
Subba Rao, T.1
Gabr, M.M.2
-
183
-
-
33645086202
-
Reversibility as a criterion for discriminating time series
-
C. Diks, J.C. van Houwelingen, F. Takens, J. DeGoede, Reversibility as a criterion for discriminating time series, Phys. Lett. A 201 (1995) 221.
-
(1995)
Phys. Lett. A
, vol.201
, pp. 221
-
-
Diks, C.1
Van Houwelingen, J.C.2
Takens, F.3
Degoede, J.4
-
184
-
-
0028477067
-
The point correlation dimension: Performance with nonstationary surrogate data and noise
-
J.E. Skinner, M. Molnar, C. Tomberg, The point correlation dimension: performance with nonstationary surrogate data and noise, Integrative Physiological Behavioral Sci. 29 (1994) 217.
-
(1994)
Integrative Physiological Behavioral Sci.
, vol.29
, pp. 217
-
-
Skinner, J.E.1
Molnar, M.2
Tomberg, C.3
-
185
-
-
0002952698
-
Significance testing on information theoretic functionals
-
M.S. Roulston, Significance testing on information theoretic functionals, Physica D 110 (1997) 62.
-
(1997)
Physica D
, vol.110
, pp. 62
-
-
Roulston, M.S.1
-
186
-
-
22244449004
-
Constrained-realization Monte-Carlo method for hypothesis testing
-
J. Theiler, D. Prichard, Constrained-realization Monte-Carlo method for hypothesis testing, Physica D 94 (1996) 221.
-
(1996)
Physica D
, vol.94
, pp. 221
-
-
Theiler, J.1
Prichard, D.2
-
187
-
-
0001318121
-
Constrained randomization of time series data
-
T. Schreiber, Constrained randomization of time series data, Phys. Rev. Lett. 80 (1998) 2105.
-
(1998)
Phys. Rev. Lett.
, vol.80
, pp. 2105
-
-
Schreiber, T.1
-
188
-
-
0003421415
-
-
SIAM, Philadelphia, PA
-
B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans, SIAM, Philadelphia, PA, 1982.
-
(1982)
The Jackknife, the Bootstrap and Other Resampling Plans
-
-
Efron, B.1
-
189
-
-
6144236430
-
Improved surrogate data for nonlinearity tests
-
T. Schreiber, A. Schmitz, Improved surrogate data for nonlinearity tests, Phys. Rev. Lett. 77 (1996) 635.
-
(1996)
Phys. Rev. Lett.
, vol.77
, pp. 635
-
-
Schreiber, T.1
Schmitz, A.2
-
191
-
-
5744249209
-
Equations of state calculations by fast computing machine
-
N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, Equations of state calculations by fast computing machine, J. Chem. Phys. 21 (1953) 1097.
-
(1953)
J. Chem. Phys.
, vol.21
, pp. 1097
-
-
Metropolis, N.1
Rosenbluth, A.2
Rosenbluth, M.3
Teller, A.4
Teller, E.5
-
193
-
-
0004137364
-
-
Springer, Berlin
-
R.V.V. Vidal (Ed.), Applied Simulated Annealing, Lecture Notes in Economics and Mathematical Systems, vol. 396, Springer, Berlin, 1993.
-
(1993)
Applied Simulated Annealing, Lecture Notes in Economics and Mathematical Systems
, vol.396
-
-
Vidal, R.V.V.1
-
194
-
-
0008973011
-
-
in [10]
-
D.R. Rigney, A.L. Goldberger, W. Ocasio, Y. Ichimaru, G.B. Moody, R. Mark, Multi-channel physiological data: description and analysis, in [10].
-
Multi-channel Physiological Data: Description and Analysis
-
-
Rigney, D.R.1
Goldberger, A.L.2
Ocasio, W.3
Ichimaru, Y.4
Moody, G.B.5
Mark, R.6
-
196
-
-
42449156579
-
Generalized autoregressive conditional heteroscedasticity
-
T. Bollerslev, Generalized autoregressive conditional heteroscedasticity, J. Econometrics 31 (1986) 207.
-
(1986)
J. Econometrics
, vol.31
, pp. 207
-
-
Bollerslev, T.1
-
197
-
-
0343506992
-
The correlation dimension of differenced data
-
D. Prichard, The correlation dimension of differenced data, Phys. Lett. A 191 (1994) 245.
-
(1994)
Phys. Lett. A
, vol.191
, pp. 245
-
-
Prichard, D.1
-
198
-
-
0002635074
-
Exploiting chaos to predict the future and reduce noise
-
Y.C. Lee (Ed.), World Scientific, Singapore
-
J.D. Farmer, J. Sidorowich, Exploiting chaos to predict the future and reduce noise, in: Y.C. Lee (Ed.), Evolution, Learning and Cognition, World Scientific, Singapore, 1988.
-
(1988)
Evolution, Learning and Cognition
-
-
Farmer, J.D.1
Sidorowich, J.2
-
199
-
-
0000621736
-
Noise reduction in dynamical systems
-
Reprinted in [5]
-
E.J. Kostelich, J.A. Yorke, Noise reduction in dynamical systems, Phys. Rev. A 38 (1988) 1649; Reprinted in [5].
-
(1988)
Phys. Rev. A
, vol.38
, pp. 1649
-
-
Kostelich, E.J.1
Yorke, J.A.2
-
200
-
-
0000097854
-
A simple noise-reduction method for real data
-
T. Schreiber, P. Grassberger, A simple noise-reduction method for real data, Phys. Lett. A 160 (1991) 411.
-
(1991)
Phys. Lett. A
, vol.160
, pp. 411
-
-
Schreiber, T.1
Grassberger, P.2
-
201
-
-
36448999076
-
On noise reduction methods for chaotic data
-
Reprinted in [5]
-
P. Grassberger, R. Hegger, H. Kantz, C. Schaffrath, T. Schreiber, On noise reduction methods for chaotic data, CHAOS 3 (1993) 127; Reprinted in [5].
-
(1993)
CHAOS
, vol.3
, pp. 127
-
-
Grassberger, P.1
Hegger, R.2
Kantz, H.3
Schaffrath, C.4
Schreiber, T.5
-
202
-
-
0001391710
-
Noise reduction in chaotic time series data: A survey of common methods
-
E.J. Kostelich, T. Schreiber, Noise reduction in chaotic time series data: a survey of common methods, Phys. Rev. E 48 (1993) 1752.
-
(1993)
Phys. Rev. E
, vol.48
, pp. 1752
-
-
Kostelich, E.J.1
Schreiber, T.2
-
205
-
-
34249988665
-
Extracting qualitative dynamics from experimental data
-
D. Broomhead, G.P. King, Extracting qualitative dynamics from experimental data, Physica D 20 (1986) 217.
-
(1986)
Physica D
, vol.20
, pp. 217
-
-
Broomhead, D.1
King, G.P.2
-
206
-
-
0038875365
-
Nonlinear noise reduction for electrocardiograms
-
T. Schreiber, D.T. Kaplan, Nonlinear noise reduction for electrocardiograms, CHAOS 6 (1996) 87.
-
(1996)
Chaos
, vol.6
, pp. 87
-
-
Schreiber, T.1
Kaplan, D.T.2
-
207
-
-
0001182355
-
Nonlinear noise reduction: A case study on experimental data
-
H. Kantz, T. Schreiber, I. Hoffmann, T. Buzug, G. Pfister, L.G. Flepp, J. Simonet, R. Badii, E. Brun, Nonlinear noise reduction: a case study on experimental data, Phys. Rev. E 48 (1993) 1529.
-
(1993)
Phys. Rev. E
, vol.48
, pp. 1529
-
-
Kantz, H.1
Schreiber, T.2
Hoffmann, I.3
Buzug, T.4
Pfister, G.5
Flepp, L.G.6
Simonet, J.7
Badii, R.8
Brun, E.9
-
208
-
-
12944259200
-
Efficient neighbor searching in nonlinear time series analysis
-
T. Schreiber, Efficient neighbor searching in nonlinear time series analysis, Int. J. Bifurcation Chaos 5 (1995) 349.
-
(1995)
Int. J. Bifurcation Chaos
, vol.5
, pp. 349
-
-
Schreiber, T.1
-
211
-
-
0001373630
-
Extremely simple nonlinear noise reduction method
-
T. Schreiber, Extremely simple nonlinear noise reduction method, Phys. Rev. E 47 (1993) 2401.
-
(1993)
Phys. Rev. E
, vol.47
, pp. 2401
-
-
Schreiber, T.1
-
212
-
-
0345983132
-
-
unpublished
-
T. Schreiber, unpublished, 1997.
-
(1997)
-
-
Schreiber, T.1
-
213
-
-
0000311114
-
Signal separation by nonlinear projections: The fetal electrocardiogram
-
T. Schreiber, D.T. Kaplan, Signal separation by nonlinear projections: the fetal electrocardiogram, Phys. Rev. E 53 (1996) 4326.
-
(1996)
Phys. Rev. E
, vol.53
, pp. 4326
-
-
Schreiber, T.1
Kaplan, D.T.2
-
215
-
-
0027967105
-
A noninvasive method for recording the electrical activity of the human uterus in vivo
-
J.F Hofmeister, J.C. Slocumb, L.M. Kottmann, J.B. Picchiottino, D.G. Ellis, A noninvasive method for recording the electrical activity of the human uterus in vivo, Biomed. Instr. Technol. (1994) 391.
-
(1994)
Biomed. Instr. Technol.
, pp. 391
-
-
Hofmeister, J.F.1
Slocumb, J.C.2
Kottmann, L.M.3
Picchiottino, J.B.4
Ellis, D.G.5
-
217
-
-
0006490006
-
Measures of spatio-temporal dynamics
-
A.M. Albano, P.E. Rapp, N.B. Abraham, A. Passamante (Eds.), Measures of spatio-temporal dynamics, Physica D 96 (1996).
-
(1996)
Physica D
, vol.96
-
-
Albano, A.M.1
Rapp, P.E.2
Abraham, N.B.3
Passamante, A.4
-
220
-
-
12044252828
-
Pattern formation outside of equilibrium
-
M.C. Cross, P.C. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. 65 (1993) 851.
-
(1993)
Rev. Mod. Phys.
, vol.65
, pp. 851
-
-
Cross, M.C.1
Hohenberg, P.C.2
-
221
-
-
0039269009
-
Inferring chaotic dynamics from time-series: On which length scale determinism becomes visible
-
E. Olbrich, H. Kantz, Inferring chaotic dynamics from time-series: On which length scale determinism becomes visible, Phys. Lett. A 232 (1997) 63.
-
(1997)
Phys. Lett. A
, vol.232
, pp. 63
-
-
Olbrich, E.1
Kantz, H.2
-
222
-
-
26344450284
-
Karhunen-Loéve decomposition of extensive chaos
-
S.M. Zoldi, H.S. Greenside, Karhunen-Loéve decomposition of extensive chaos, Phys. Rev. Lett. 78 (1997) 9.
-
(1997)
Phys. Rev. Lett.
, vol.78
, pp. 9
-
-
Zoldi, S.M.1
Greenside, H.S.2
-
223
-
-
0002833349
-
Reconstrution of the spatio-temporal dynamics of a human magnetoencephalogram
-
V.K. Jirsa, R. Friedrich, H. Haken, Reconstrution of the spatio-temporal dynamics of a human magnetoencephalogram, Physica D 89 (1995) 100.
-
(1995)
Physica D
, vol.89
, pp. 100
-
-
Jirsa, V.K.1
Friedrich, R.2
Haken, H.3
-
224
-
-
0002099058
-
Hopf's last hope: Spatiotemporal chaos in terms of unstable recurrent patterns
-
F. Christiansen, P. Cvitanović, V. Putkaradze, Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns, Nonlinearity 10 (1997) 1.
-
(1997)
Nonlinearity
, vol.10
, pp. 1
-
-
Christiansen, F.1
Cvitanović, P.2
Putkaradze, V.3
-
225
-
-
0032028875
-
Spatially localized unstable periodic orbits of a high-dimensional chaotic system
-
S.M. Zoldi, H.S. Greenside, Spatially localized unstable periodic orbits of a high-dimensional chaotic system, Phys. Rev. E 57 (1998) R2511.
-
(1998)
Phys. Rev. E
, vol.57
-
-
Zoldi, S.M.1
Greenside, H.S.2
-
226
-
-
0042148724
-
Tool to recover scalar time-delay systems from experimental time series
-
M.J. Bünner, M. Popp, Th. Meyer, A. Kittel, J. Parisi, Tool to recover scalar time-delay systems from experimental time series, Phys. Rev. E 54 (1996) 3082.
-
(1996)
Phys. Rev. E
, vol.54
, pp. 3082
-
-
Bünner, M.J.1
Popp, M.2
Meyer, Th.3
Kittel, A.4
Parisi, J.5
-
227
-
-
35949018382
-
Ergodic theory of chaos and strange attractors
-
J.-P. Eckmann, D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57 (1985) 617.
-
(1985)
Rev. Mod. Phys.
, vol.57
, pp. 617
-
-
Eckmann, J.-P.1
Ruelle, D.2
-
228
-
-
0001870459
-
The dynamics of the Hénon map
-
M. Benedicks, L. Carleson, The dynamics of the Hénon map, Ann. Math. 133 (1991) 73.
-
(1991)
Ann. Math.
, vol.133
, pp. 73
-
-
Benedicks, M.1
Carleson, L.2
-
229
-
-
0031490957
-
Are the dimensions of a set and its image equal under typical smooth functions?
-
T. Sauer, J. Yorke, Are the dimensions of a set and its image equal under typical smooth functions? Ergodic Th. Dyn. Syst. 17 (1997) 941.
-
(1997)
Ergodic Th. Dyn. Syst.
, vol.17
, pp. 941
-
-
Sauer, T.1
Yorke, J.2
-
230
-
-
0001337517
-
Resonances of chaotic dynamical systems
-
D. Ruelle, Resonances of chaotic dynamical systems, Phys. Rev. Lett. 56 (1986) 405.
-
(1986)
Phys. Rev. Lett.
, vol.56
, pp. 405
-
-
Ruelle, D.1
-
231
-
-
0000011469
-
Resonances for intermittent systems
-
V. Baladi, J.-P. Eckmann, Resonances for intermittent systems, Nonlinearity 2 (1989) 119.
-
(1989)
Nonlinearity
, vol.2
, pp. 119
-
-
Baladi, V.1
Eckmann, J.-P.2
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