-
1
-
-
34249834828
-
Local Lyapunov exponents from observed data
-
H.D.I. Abarbanel, R. Brown, M.B. Kennel, Local Lyapunov exponents from observed data, J. Nonlinear Sci. 2 (1992) 343-365; H.D.I. Abarbanel, R. Brown, J.L. Sidorowich, L.L. Tsimring, The analysis of observed chaotic data in physical systems, Rev. Mod. Phys. 65 (1993) 1331-1392.
-
(1992)
J. Nonlinear Sci.
, vol.2
, pp. 343-365
-
-
Abarbanel, H.D.I.1
Brown, R.2
Kennel, M.B.3
-
2
-
-
12044249591
-
The analysis of observed chaotic data in physical systems
-
H.D.I. Abarbanel, R. Brown, M.B. Kennel, Local Lyapunov exponents from observed data, J. Nonlinear Sci. 2 (1992) 343-365; H.D.I. Abarbanel, R. Brown, J.L. Sidorowich, L.L. Tsimring, The analysis of observed chaotic data in physical systems, Rev. Mod. Phys. 65 (1993) 1331-1392.
-
(1993)
Rev. Mod. Phys.
, vol.65
, pp. 1331-1392
-
-
Abarbanel, H.D.I.1
Brown, R.2
Sidorowich, J.L.3
Tsimring, L.L.4
-
3
-
-
35949011725
-
Singular value decomposition and the Grassberger-Procaccia algorithm
-
A.M. Albano, J. Muench, C. Schwartz, A.I. Mees, P.E. Rapp, Singular value decomposition and the Grassberger-Procaccia algorithm, Phys. Rev. A 38 (1988) 3017-3026.
-
(1988)
Phys. Rev. A
, vol.38
, pp. 3017-3026
-
-
Albano, A.M.1
Muench, J.2
Schwartz, C.3
Mees, A.I.4
Rapp, P.E.5
-
4
-
-
0003568098
-
-
Springer, New York
-
K.T. Alligood, T. Sauer, J.A. Yorke, Chaos: An Introduction to Dynamical Systems, Springer, New York, 1996.
-
(1996)
Chaos: An Introduction to Dynamical Systems
-
-
Alligood, K.T.1
Sauer, T.2
Yorke, J.A.3
-
5
-
-
0011662662
-
Chemical chaos: From hints to confirmation
-
F. Argoul, A. Arneodo, P. Richetti, J.C. Roux, Chemical chaos: from hints to confirmation. Accounts Chem. Res. 20 (1987) 436-442.
-
(1987)
Accounts Chem. Res.
, vol.20
, pp. 436-442
-
-
Argoul, F.1
Arneodo, A.2
Richetti, P.3
Roux, J.C.4
-
6
-
-
0000357105
-
Dimension increase in filtered chaotic signals
-
R. Badii, G. Broggi, B. Derighetti, M. Ravani, S. Ciliberto, A. Politi, M.A. Rubio, Dimension increase in filtered chaotic signals, Phys. Rev. Lett. 60 (1988) 979-982; D.S. Broomhead, J.P. Huke, M.R. Muldoon, Linear filters and nonlinear systems, J. Roy. Statist. Soc. B 54 (1992) 373-382; Milan Pauluš and Ivan Dvořák, Singular value decomposition in attractor reconstruction: pitfalls and precautions, Physica D 55 (1992) 221-234.
-
(1988)
Phys. Rev. Lett.
, vol.60
, pp. 979-982
-
-
Badii, R.1
Broggi, G.2
Derighetti, B.3
Ravani, M.4
Ciliberto, S.5
Politi, A.6
Rubio, M.A.7
-
7
-
-
0000357105
-
Linear filters and nonlinear systems
-
R. Badii, G. Broggi, B. Derighetti, M. Ravani, S. Ciliberto, A. Politi, M.A. Rubio, Dimension increase in filtered chaotic signals, Phys. Rev. Lett. 60 (1988) 979-982; D.S. Broomhead, J.P. Huke, M.R. Muldoon, Linear filters and nonlinear systems, J. Roy. Statist. Soc. B 54 (1992) 373-382; Milan Pauluš and Ivan Dvořák, Singular value decomposition in attractor reconstruction: pitfalls and precautions, Physica D 55 (1992) 221-234.
-
(1992)
J. Roy. Statist. Soc. B
, vol.54
, pp. 373-382
-
-
Broomhead, D.S.1
Huke, J.P.2
Muldoon, M.R.3
-
8
-
-
0000936320
-
Singular value decomposition in attractor reconstruction: Pitfalls and precautions
-
R. Badii, G. Broggi, B. Derighetti, M. Ravani, S. Ciliberto, A. Politi, M.A. Rubio, Dimension increase in filtered chaotic signals, Phys. Rev. Lett. 60 (1988) 979-982; D.S. Broomhead, J.P. Huke, M.R. Muldoon, Linear filters and nonlinear systems, J. Roy. Statist. Soc. B 54 (1992) 373-382; Milan Pauluš and Ivan Dvořák, Singular value decomposition in attractor reconstruction: pitfalls and precautions, Physica D 55 (1992) 221-234.
-
(1992)
Physica D
, vol.55
, pp. 221-234
-
-
Pauluš, M.1
Dvořák, I.2
-
9
-
-
0000510147
-
Detection of nonlinear dynamics in short, noisy time series
-
M. Barahona, Ch.-S. Poon, Detection of nonlinear dynamics in short, noisy time series, Nature 381 (1996) 215-217.
-
(1996)
Nature
, vol.381
, pp. 215-217
-
-
Barahona, M.1
Poon, Ch.-S.2
-
10
-
-
34249988665
-
Extracting qualitative dynamics from experimental data
-
D.S. Broomhead, G.P. King, Extracting qualitative dynamics from experimental data, Physica D 20 (1986) 217-236.
-
(1986)
Physica D
, vol.20
, pp. 217-236
-
-
Broomhead, D.S.1
King, G.P.2
-
11
-
-
0000416890
-
Topological dimension and local coordinates from time series
-
D.S. Broomhead, R. Jones, G.P. King, Topological dimension and local coordinates from time series, J. Phys. A 20 (1987) L563.
-
(1987)
J. Phys. A
, vol.20
-
-
Broomhead, D.S.1
Jones, R.2
King, G.P.3
-
12
-
-
22244456151
-
Strange attractors in weakly turbulent Couette-Taylor flow
-
A. Brandstater, H.L. Swinney, Strange attractors in weakly turbulent Couette-Taylor flow, Phys. Rev. A 35 (1987) 2207-2220.
-
(1987)
Phys. Rev. A
, vol.35
, pp. 2207-2220
-
-
Brandstater, A.1
Swinney, H.L.2
-
13
-
-
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) 52-98.
-
(1991)
Physica D
, vol.51
, pp. 52-98
-
-
Casdagli, M.1
Eubank, S.2
Farmer, J.D.3
Gibson, J.4
-
15
-
-
0000822478
-
Plateau onset of correlation dimension: When does it occur?
-
M. Ding, C. Grebogi, E. Ott, T. Sauer, J.A. Yorke, Plateau onset of correlation dimension: when does it occur?, Phys. Rev. Lett. 70 (1993) 3872-3875.
-
(1993)
Phys. Rev. Lett.
, vol.70
, pp. 3872-3875
-
-
Ding, M.1
Grebogi, C.2
Ott, E.3
Sauer, T.4
Yorke, J.A.5
-
16
-
-
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) 617-656.
-
(1985)
Rev. Mod. Phys.
, vol.57
, pp. 617-656
-
-
Eckmann, J.-P.1
Ruelle, D.2
-
18
-
-
0018515437
-
Dynamical instabilities and the transition to chaotic Taylor vortex flow
-
P.R. Fenstermacher, H.L. Swinney, J.P. Gollub, Dynamical instabilities and the transition to chaotic Taylor vortex flow, J. Fluid Mech. 94 (1979) 103-128.
-
(1979)
J. Fluid Mech.
, vol.94
, pp. 103-128
-
-
Fenstermacher, P.R.1
Swinney, H.L.2
Gollub, J.P.3
-
19
-
-
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) 1134-1140.
-
(1986)
Phys. Rev. A
, vol.33
, pp. 1134-1140
-
-
Fraser, A.M.1
Swinney, H.L.2
-
20
-
-
40749093037
-
Measuring the strangeness of strange attractors
-
P. Grassberger, I. Procaccia, Measuring the strangeness of strange attractors, Physica D 9 (1983) 189-208.
-
(1983)
Physica D
, vol.9
, pp. 189-208
-
-
Grassberger, P.1
Procaccia, I.2
-
21
-
-
0003743332
-
-
World Scientific, Singapore
-
B.-L. Hao (Ed.), Chaos II, World Scientific, Singapore, 1990.
-
(1990)
Chaos II
-
-
Hao, B.-L.1
-
22
-
-
11944266815
-
Direct test for determinism in a time series
-
D.T. Kaplan, L. Glass, Direct test for determinism in a time series, Phys. Rev. Lett. 68 (1992) 427-430; D.T. Kaplan, Exceptional events as evidence for determinism, Physica D 73 (1994) 38-48.
-
(1992)
Phys. Rev. Lett.
, vol.68
, pp. 427-430
-
-
Kaplan, D.T.1
Glass, L.2
-
23
-
-
29444452036
-
Exceptional events as evidence for determinism
-
D.T. Kaplan, L. Glass, Direct test for determinism in a time series, Phys. Rev. Lett. 68 (1992) 427-430; D.T. Kaplan, Exceptional events as evidence for determinism, Physica D 73 (1994) 38-48.
-
(1994)
Physica D
, vol.73
, pp. 38-48
-
-
Kaplan, D.T.1
-
25
-
-
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) 1752-1762.
-
(1993)
Phys. Rev. E
, vol.48
, pp. 1752-1762
-
-
Kostelich, E.J.1
Schreiber, T.2
-
26
-
-
4143093387
-
Characterization of a strange attractor by periodic orbits
-
D.P. Lathrop, E.J. Kostelich, Characterization of a strange attractor by periodic orbits, Phys. Rev. A 40 (1989) 4028-4031.
-
(1989)
Phys. Rev. A
, vol.40
, pp. 4028-4031
-
-
Lathrop, D.P.1
Kostelich, E.J.2
-
27
-
-
0000241853
-
Deterministic nonperiodic flow
-
E.N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci. 20 (1963) 130-141.
-
(1963)
J. Atmos. Sci.
, vol.20
, pp. 130-141
-
-
Lorenz, E.N.1
-
29
-
-
0003582543
-
-
Cambridge University Press, Cambridge
-
E. Ott, Chaos in Dynamical Systems, Cambridge University Press, Cambridge, 1993.
-
(1993)
Chaos in Dynamical Systems
-
-
Ott, E.1
-
31
-
-
0001235864
-
Observation of a strange attractor
-
J.C. Roux, R.H. Simoyi, H.L. Swinney, Observation of a strange attractor, Physica D 8 (1983) 257-265; K. Coffman, W.D. McCormick, Z. Noszticzius, R.H. Simoyi, H.L. Swinney, Universality, multiplicity, and the effect of iron impurities in the Belousov-Zhabotinskii reaction, J. Chem. Phys. 86 (1987) 119-129.
-
(1983)
Physica D
, vol.8
, pp. 257-265
-
-
Roux, J.C.1
Simoyi, R.H.2
Swinney, H.L.3
-
32
-
-
5244219773
-
Universality, multiplicity, and the effect of iron impurities in the Belousov-Zhabotinskii reaction
-
J.C. Roux, R.H. Simoyi, H.L. Swinney, Observation of a strange attractor, Physica D 8 (1983) 257-265; K. Coffman, W.D. McCormick, Z. Noszticzius, R.H. Simoyi, H.L. Swinney, Universality, multiplicity, and the effect of iron impurities in the Belousov-Zhabotinskii reaction, J. Chem. Phys. 86 (1987) 119-129.
-
(1987)
J. Chem. Phys.
, vol.86
, pp. 119-129
-
-
Coffman, K.1
McCormick, W.D.2
Noszticzius, Z.3
Simoyi, R.H.4
Swinney, H.L.5
-
34
-
-
44049113048
-
A noise reduction method for signals from non-linear systems
-
T. Sauer, A noise reduction method for signals from non-linear systems, Physica D 58 (1992) 193-201.
-
(1992)
Physica D
, vol.58
, pp. 193-201
-
-
Sauer, T.1
-
35
-
-
46149128981
-
Distinguished random and deterministic systems: Abridged version
-
See, for instance, W.A. Brock, Distinguished random and deterministic systems: abridged version. J. Economic Theory 40 (1986) 168-195; W.A. Brock, W.B. Dechert, Theorems on distinguishing deterministic from random systems, in: W.A. Barnett, E.R. Berndt, H. White (Eds.), Dynamic Econometric Modeling, Cambridge University Press, Cambridge, 1988, pp. 247-268; W.A. Brock, D.A. Hsieh, B. LeBaron, Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence, MIT Press, Cambridge, MA, 1991.
-
(1986)
J. Economic Theory
, vol.40
, pp. 168-195
-
-
Brock, W.A.1
-
36
-
-
46149128981
-
Theorems on distinguishing deterministic from random systems
-
W.A. Barnett, E.R. Berndt, H. White (Eds.), Cambridge University Press, Cambridge
-
See, for instance, W.A. Brock, Distinguished random and deterministic systems: abridged version. J. Economic Theory 40 (1986) 168-195; W.A. Brock, W.B. Dechert, Theorems on distinguishing deterministic from random systems, in: W.A. Barnett, E.R. Berndt, H. White (Eds.), Dynamic Econometric Modeling, Cambridge University Press, Cambridge, 1988, pp. 247-268; W.A. Brock, D.A. Hsieh, B. LeBaron, Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence, MIT Press, Cambridge, MA, 1991.
-
(1988)
Dynamic Econometric Modeling
, pp. 247-268
-
-
Brock, W.A.1
Dechert, W.B.2
-
37
-
-
46149128981
-
-
MIT Press, Cambridge, MA
-
See, for instance, W.A. Brock, Distinguished random and deterministic systems: abridged version. J. Economic Theory 40 (1986) 168-195; W.A. Brock, W.B. Dechert, Theorems on distinguishing deterministic from random systems, in: W.A. Barnett, E.R. Berndt, H. White (Eds.), Dynamic Econometric Modeling, Cambridge University Press, Cambridge, 1988, pp. 247-268; W.A. Brock, D.A. Hsieh, 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
Hsieh, D.A.2
LeBaron, B.3
-
39
-
-
11944254388
-
Controlling chaos using time delay coordinates
-
See, for instance, U. Dressler, G. Nitsche, Controlling chaos using time delay coordinates, Phys. Rev. Lett. 68 (1992) 1; T. Shinbrot, W. Ditto, C. Grebogi, E. Ott, M.L. Spano, J.A. Yorke, Using the sensitive dependence of chaos (the 'butterfly effect') to direct trajectories in an experimental chaotic system, Phys. Rev. Lett. 68 (1992) 2863-2866; In: W. Ditto, M.L. Spano, Adaptive control and tracking of chaos in a magnetoelastic ribbon, Phys. Rev. E 51 (1995) 2689-2692; E. Ott, Recent developments in chaotic dynamics, IEEE Trans. Plasma Sci. 22 (1994) 43-46; V. Petrov, E. Mihaliuk, S.K. Scott, K. Showalter, Stabilizing and characterizing unstable states in high- dimensional systems from time series, Phys. Rev. E 51 (1995) 3988-3996.
-
(1992)
Phys. Rev. Lett.
, vol.68
, pp. 1
-
-
Dressler, U.1
Nitsche, G.2
-
40
-
-
0000301863
-
Using the sensitive dependence of chaos (the 'butterfly effect') to direct trajectories in an experimental chaotic system
-
See, for instance, U. Dressler, G. Nitsche, Controlling chaos using time delay coordinates, Phys. Rev. Lett. 68 (1992) 1; T. Shinbrot, W. Ditto, C. Grebogi, E. Ott, M.L. Spano, J.A. Yorke, Using the sensitive dependence of chaos (the 'butterfly effect') to direct trajectories in an experimental chaotic system, Phys. Rev. Lett. 68 (1992) 2863-2866; In: W. Ditto, M.L. Spano, Adaptive control and tracking of chaos in a magnetoelastic ribbon, Phys. Rev. E 51 (1995) 2689-2692; E. Ott, Recent developments in chaotic dynamics, IEEE Trans. Plasma Sci. 22 (1994) 43-46; V. Petrov, E. Mihaliuk, S.K. Scott, K. Showalter, Stabilizing and characterizing unstable states in high- dimensional systems from time series, Phys. Rev. E 51 (1995) 3988-3996.
-
(1992)
Phys. Rev. Lett.
, vol.68
, pp. 2863-2866
-
-
Shinbrot, T.1
Ditto, W.2
Grebogi, C.3
Ott, E.4
Spano, M.L.5
Yorke, J.A.6
-
41
-
-
0002270984
-
Adaptive control and tracking of chaos in a magnetoelastic ribbon
-
See, for instance, U. Dressler, G. Nitsche, Controlling chaos using time delay coordinates, Phys. Rev. Lett. 68 (1992) 1; T. Shinbrot, W. Ditto, C. Grebogi, E. Ott, M.L. Spano, J.A. Yorke, Using the sensitive dependence of chaos (the 'butterfly effect') to direct trajectories in an experimental chaotic system, Phys. Rev. Lett. 68 (1992) 2863-2866; In: W. Ditto, M.L. Spano, Adaptive control and tracking of chaos in a magnetoelastic ribbon, Phys. Rev. E 51 (1995) 2689-2692; E. Ott, Recent developments in chaotic dynamics, IEEE Trans. Plasma Sci. 22 (1994) 43-46; V. Petrov, E. Mihaliuk, S.K. Scott, K. Showalter, Stabilizing and characterizing unstable states in high- dimensional systems from time series, Phys. Rev. E 51 (1995) 3988-3996.
-
(1995)
Phys. Rev. E
, vol.51
, pp. 2689-2692
-
-
Ditto, W.1
Spano, M.L.2
-
42
-
-
0028381117
-
Recent developments in chaotic dynamics
-
See, for instance, U. Dressler, G. Nitsche, Controlling chaos using time delay coordinates, Phys. Rev. Lett. 68 (1992) 1; T. Shinbrot, W. Ditto, C. Grebogi, E. Ott, M.L. Spano, J.A. Yorke, Using the sensitive dependence of chaos (the 'butterfly effect') to direct trajectories in an experimental chaotic system, Phys. Rev. Lett. 68 (1992) 2863-2866; In: W. Ditto, M.L. Spano, Adaptive control and tracking of chaos in a magnetoelastic ribbon, Phys. Rev. E 51 (1995) 2689-2692; E. Ott, Recent developments in chaotic dynamics, IEEE Trans. Plasma Sci. 22 (1994) 43-46; V. Petrov, E. Mihaliuk, S.K. Scott, K. Showalter, Stabilizing and characterizing unstable states in high- dimensional systems from time series, Phys. Rev. E 51 (1995) 3988-3996.
-
(1994)
IEEE Trans. Plasma Sci.
, vol.22
, pp. 43-46
-
-
Ott, E.1
-
43
-
-
0040328751
-
Stabilizing and characterizing unstable states in high-dimensional systems from time series
-
See, for instance, U. Dressler, G. Nitsche, Controlling chaos using time delay coordinates, Phys. Rev. Lett. 68 (1992) 1; T. Shinbrot, W. Ditto, C. Grebogi, E. Ott, M.L. Spano, J.A. Yorke, Using the sensitive dependence of chaos (the 'butterfly effect') to direct trajectories in an experimental chaotic system, Phys. Rev. Lett. 68 (1992) 2863-2866; In: W. Ditto, M.L. Spano, Adaptive control and tracking of chaos in a magnetoelastic ribbon, Phys. Rev. E 51 (1995) 2689-2692; E. Ott, Recent developments in chaotic dynamics, IEEE Trans. Plasma Sci. 22 (1994) 43-46; V. Petrov, E. Mihaliuk, S.K. Scott, K. Showalter, Stabilizing and characterizing unstable states in high-dimensional systems from time series, Phys. Rev. E 51 (1995) 3988-3996.
-
(1995)
Phys. Rev. E
, vol.51
, pp. 3988-3996
-
-
Petrov, V.1
Mihaliuk, E.2
Scott, S.K.3
Showalter, K.4
-
44
-
-
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) 4705-4708.
-
(1996)
Phys. Rev. Lett.
, vol.76
, pp. 4705-4708
-
-
So, P.1
Ott, E.2
Schiff, S.J.3
Kaplan, D.T.4
Sauer, T.5
Grebogi, C.6
-
46
-
-
0000779360
-
Detecting Strange Attractors in Turbulence
-
A. Dold and B. Eckmann (Eds.), Dynamical Systems and Turbulence, Warwick, 1980. Springer, Berlin
-
F. Takens, Detecting Strange Attractors in Turbulence, in: A. Dold and B. Eckmann (Eds.), Dynamical Systems and Turbulence, Warwick, 1980. Lecture Notes in Mathematics, vol. 898, Springer, Berlin, 1981, pp. 366-381.
-
(1981)
Lecture Notes in Mathematics
, vol.898
, pp. 366-381
-
-
Takens, F.1
-
47
-
-
44049111332
-
Testing for nonlinearity in time series: The method of surrogate data
-
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) 77-94.
-
(1992)
Physica D
, vol.58
, pp. 77-94
-
-
Theiler, J.1
Eubank, S.2
Longtin, A.3
Galdrikian, B.4
Farmer, J.D.5
-
48
-
-
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) 285-317.
-
(1985)
Physica D
, vol.16
, pp. 285-317
-
-
Wolf, A.1
Swift, J.B.2
Swinney, H.L.3
Vastano, J.A.4
|