메뉴 건너뛰기




Volumn 2009, Issue , 2009, Pages

Modeling nonlinear dynamics and chaos: A review

Author keywords

[No Author keywords available]

Indexed keywords

DATA REQUIREMENTS; ESTIMATION TECHNIQUES; KEY TOPICS; MODEL REPRESENTATION; MODEL VALIDATION; MODELING TECHNIQUE; NON-LINEAR DYNAMICS;

EID: 67651049732     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2009/238960     Document Type: Review
Times cited : (135)

References (237)
  • 1
    • 0001277779 scopus 로고
    • Sur les courbes dfinies par une quation diffrentielle
    • Poincar H., Sur les courbes dfinies par une quation diffrentielle Journal de Mathmatiques Pures et Appliques 1885 4 1 167 244
    • (1885) Journal de Mathmatiques Pures et Appliques , vol.4 , Issue.1 , pp. 167-244
    • Poincar, H.1
  • 3
    • 0004252991 scopus 로고
    • Oxford, UK Pergamon Press Traduction anglaise par F. Immirzi, Dover, New York, NY, USA, 1937
    • Andronov A. A., Vitt A. A., Khaikin S. E., Theory of Oscillators 1966 Oxford, UK Pergamon Press xxxii+815. Traduction anglaise par F. Immirzi, Dover, New York, NY, USA, 1937
    • (1966) Theory of Oscillators , pp. 815
    • Andronov, A.A.1    Vitt, A.A.2    Khaikin, S.E.3
  • 6
    • 0016394337 scopus 로고
    • Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos
    • May R. M., Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos Science 1974 186 4164 645 647
    • (1974) Science , vol.186 , Issue.4164 , pp. 645-647
    • May, R.M.1
  • 7
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • Rssler O. E., An equation for continuous chaos Physics Letters A 1976 57 5 397 398
    • (1976) Physics Letters A , vol.57 , Issue.5 , pp. 397-398
    • Rssler, O.E.1
  • 11
    • 0003290175 scopus 로고
    • On the dimension of the compact invariant sets of certain nonlinear maps
    • Berlin, Germany Springer Lecture Notes in Mathematics
    • Ma R., Rand D. A., Young L. S., On the dimension of the compact invariant sets of certain nonlinear maps Dynamical Systems and Turbulence, Warwick 1980 (Coventry, 1979/1980) 1981 898 Berlin, Germany Springer 230 242 Lecture Notes in Mathematics
    • (1981) Dynamical Systems and Turbulence, Warwick 1980 (Coventry, 1979/1980) , vol.898 , pp. 230-242
    • Ma, R.1    Rand, D.A.2    Young, L.S.3
  • 12
    • 44949273552 scopus 로고
    • State space reconstruction in the presence of noise
    • Casdagli M., Eubank S., Farmer J. D., Gibson J., State space reconstruction in the presence of noise Physica D 1991 51 13 52 98
    • (1991) Physica D , vol.51 , Issue.13 , pp. 52-98
    • Casdagli, M.1    Eubank, S.2    Farmer, J.D.3    Gibson, J.4
  • 14
    • 48749145669 scopus 로고
    • The dimension of chaotic attractors
    • Farmer J. D., Ott E., Yorke J. A., The dimension of chaotic attractors Physica D 1983 7 13 153 180
    • (1983) Physica D , vol.7 , Issue.13 , pp. 153-180
    • Farmer, J.D.1    Ott, E.2    Yorke, J.A.3
  • 16
    • 0038434713 scopus 로고
    • A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems
    • Oseledec V. I., A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems Transactions of the Moscow Mathematical Society 1968 19 179 210
    • (1968) Transactions of the Moscow Mathematical Society , vol.19 , pp. 179-210
    • Oseledec, V.I.1
  • 17
    • 0001450585 scopus 로고
    • A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces
    • Kolmogorov A. N., A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces Doklady Akademii Nauk SSSR 1958 119 5 861 864
    • (1958) Doklady Akademii Nauk SSSR , vol.119 , Issue.5 , pp. 861-864
    • Kolmogorov, A.N.1
  • 20
    • 0002437378 scopus 로고
    • Nonlinear modeling of chaotic time series: theory and applications
    • chapter 15 New York, NY, USA John Wiley Sons Wiley-Interscience Publication
    • Casdagli M., Des Jardins D., Eubank S., Kim J. H., Stringer J., Nonlinear modeling of chaotic time series: theory and applications Applied Chaos 1992 chapter 15 New York, NY, USA John Wiley Sons 335 380 Wiley-Interscience Publication
    • (1992) Applied Chaos , pp. 335-380
    • Casdagli, M.1    Des Jardins, D.2    Eubank, S.3    Kim, J.H.4    Stringer, J.5
  • 23
    • 1642276131 scopus 로고    scopus 로고
    • Optimal expansions of discrete-time Volterra models using Laguerre functions
    • Campello R. J. G. B., Favier G., do Amaral W. C., Optimal expansions of discrete-time Volterra models using Laguerre functions Automatica 2004 40 5 815 822
    • (2004) Automatica , vol.40 , Issue.5 , pp. 815-822
    • Campello, R.J.G.B.1    Favier, G.2    Do Amaral, W.C.3
  • 24
    • 0019082388 scopus 로고
    • Identification of nonlinear systemsa survey
    • Billings S. A., Identification of nonlinear systemsa survey IEE Proceedings D 1980 127 6 272 285
    • (1980) IEE Proceedings D , vol.127 , Issue.6 , pp. 272-285
    • Billings, S.A.1
  • 25
    • 0022011215 scopus 로고
    • INPUT-OUTPUT PARAMETRIC MODELS FOR NON-LINEAR SYSTEMS. PART II: STOCHASTIC NON-LINEAR SYSTEMS.
    • Leontaritis I. J., Billings S. A., Input-output parametric models for nonlinear systemspart II: stochastic nonlinear systems International Journal of Control 1985 41 2 329 344 (Pubitemid 15476364)
    • (1985) International Journal of Control , vol.41 , Issue.2 , pp. 329-344
    • Leontaritis, I.J.1    Billings, S.A.2
  • 26
    • 0026218753 scopus 로고
    • Rational model identification using an extended least-squares algorithm
    • Billings S. A., Zhu Q. M., Rational model identification using an extended least-squares algorithm International Journal of Control 1991 54 3 529 546 (Pubitemid 21695779)
    • (1991) International Journal of Control , vol.54 , Issue.3 , pp. 529-546
    • Billings, S.A.1    Zhu, Q.M.2
  • 27
    • 0025399567 scopus 로고
    • Identification and control of dynamical systems using neural networks
    • DOI 10.1109/72.80202
    • Narendra K. S., Parthasarathy K., Identification and control of dynamical systems using neural networks IEEE Transactions on Neural Networks 1990 1 1 4 27 (Pubitemid 20689507)
    • (1990) IEEE Transactions on Neural Networks , vol.1 , Issue.1 , pp. 4-27
    • Narendra Kumpati, S.1    Parthasarathy Kannan2
  • 28
    • 0026116468 scopus 로고
    • Orthogonal least squares learning algorithm for radial basis function networks
    • Chen S., Cowan C. F. N., Grant P. M., Orthogonal least squares learning algorithm for radial basis function networks IEEE Transactions on Neural Networks 1991 2 2 302 309
    • (1991) IEEE Transactions on Neural Networks , vol.2 , Issue.2 , pp. 302-309
    • Chen, S.1    Cowan, C.F.N.2    Grant, P.M.3
  • 29
    • 58149210009 scopus 로고
    • Predicting chaotic time series with wavelet networks
    • Cao L., Hong Y., Fang H., He G., Predicting chaotic time series with wavelet networks Physica D 1995 85 1-2 225 238
    • (1995) Physica D , vol.85 , Issue.12 , pp. 225-238
    • Cao, L.1    Hong, Y.2    Fang, H.3    He, G.4
  • 30
    • 41549151950 scopus 로고    scopus 로고
    • An extended orthogonal forward regression algorithm for system identification using entropy
    • Guo L. Z., Billings S. A., Zhu D. Q., An extended orthogonal forward regression algorithm for system identification using entropy International Journal of Control 2008 81 4 690 699
    • (2008) International Journal of Control , vol.81 , Issue.4 , pp. 690-699
    • Guo, L.Z.1    Billings, S.A.2    Zhu, D.Q.3
  • 31
    • 41849127835 scopus 로고    scopus 로고
    • An adaptive orthogonal search algorithm for model subset selection and non-linear system identification
    • Billings S. A., Wei H. L., An adaptive orthogonal search algorithm for model subset selection and non-linear system identification International Journal of Control 2008 81 5 714 724
    • (2008) International Journal of Control , vol.81 , Issue.5 , pp. 714-724
    • Billings, S.A.1    Wei, H.L.2
  • 32
    • 53649108664 scopus 로고    scopus 로고
    • Model structure selection using an integrated forward orthogonal search algorithm assisted by squared correlation and mutual information
    • Wei H.-L., Billings S. A., Model structure selection using an integrated forward orthogonal search algorithm assisted by squared correlation and mutual information International Journal of Modelling, Identification and Control 2008 3 4 341 356
    • (2008) International Journal of Modelling, Identification and Control , vol.3 , Issue.4 , pp. 341-356
    • Wei, H.-L.1    Billings, S.A.2
  • 37
    • 0001192821 scopus 로고
    • Equations of motion from a data series
    • Crutchfield J. P., McNamara B. S., Equations of motion from a data series Complex Systems 1987 1 3 417 452
    • (1987) Complex Systems , vol.1 , Issue.3 , pp. 417-452
    • Crutchfield, J.P.1    Mcnamara, B.S.2
  • 38
    • 0000621802 scopus 로고
    • Multivariable functional interpolation and adaptive networks
    • Broomhead D. S., Lowe D., Multivariable functional interpolation and adaptive networks Complex Systems 1988 2 3 321 355
    • (1988) Complex Systems , vol.2 , Issue.3 , pp. 321-355
    • Broomhead, D.S.1    Lowe, D.2
  • 39
    • 45149144372 scopus 로고
    • Nonlinear prediction of chaotic time series
    • Casdagli M., Nonlinear prediction of chaotic time series Physica D 1989 35 3 335 356
    • (1989) Physica D , vol.35 , Issue.3 , pp. 335-356
    • Casdagli, M.1
  • 40
    • 67349186115 scopus 로고
    • Construction of differential equations from experimental data
    • Cremers J., Hbler A., Construction of differential equations from experimental data Zeitschrift fr Naturforschung A 1987 42 8 797 802
    • (1987) Zeitschrift fr Naturforschung A , vol.42 , Issue.8 , pp. 797-802
    • Cremers, J.1    Hbler, A.2
  • 41
    • 0002635074 scopus 로고
    • Exploiting chaos to predict the future and reduce noise
    • Teaneck, NJ, USA World Scientific
    • Farmer J. D., Sidorowich J. J., Lee Y. C., Exploiting chaos to predict the future and reduce noise Evolution, Learning and Cognition 1988 Teaneck, NJ, USA World Scientific 277 330
    • (1988) Evolution, Learning and Cognition , pp. 277-330
    • Farmer, J.D.1    Sidorowich, J.J.2    Lee, Y.C.3
  • 42
    • 0000202504 scopus 로고
    • Chaos and deterministic versus stochastic nonlinear modelling
    • Casdagli M., Chaos and deterministic versus stochastic nonlinear modelling Journal of the Royal Statistical Society. Series B 1992 54 2 303 328
    • (1992) Journal of the Royal Statistical Society. Series B , vol.54 , Issue.2 , pp. 303-328
    • Casdagli, M.1
  • 43
    • 35949012282 scopus 로고
    • Prediction in chaotic nonlinear systems: methods for time series with broadband Fourier spectra
    • Abarbanel H. D. I., Brown R., Kadtke J. B., Prediction in chaotic nonlinear systems: methods for time series with broadband Fourier spectra Physical Review A 1990 41 4 1782 1807
    • (1990) Physical Review A , vol.41 , Issue.4 , pp. 1782-1807
    • Abarbanel, H.D.I.1    Brown, R.2    Kadtke, J.B.3
  • 44
    • 0001282028 scopus 로고
    • Method to distinguish possible chaos from colored noise and to determine embedding parameters
    • Kennel M. B., Isabelle S., Method to distinguish possible chaos from colored noise and to determine embedding parameters Physical Review A 1992 46 6 3111 3118
    • (1992) Physical Review A , vol.46 , Issue.6 , pp. 3111-3118
    • Kennel, M.B.1    Isabelle, S.2
  • 45
    • 0001399870 scopus 로고
    • An efficient method of forecasting chaotic time series using linear interpolation
    • Linsay P. S., An efficient method of forecasting chaotic time series using linear interpolation Physics Letters A 1991 153 6-7 353 356
    • (1991) Physics Letters A , vol.153 , Issue.67 , pp. 353-356
    • Linsay, P.S.1
  • 47
    • 0001778461 scopus 로고    scopus 로고
    • Dynamics from multivariate time series
    • PII S0167278998001511
    • Cao L., Mees A., Judd K., Dynamics from multivariate time series Physica D 1998 121 1-2 75 88 (Pubitemid 128636753)
    • (1998) Physica D: Nonlinear Phenomena , vol.121 , Issue.1-2 , pp. 75-88
    • Cao, L.1    Mees, A.2    Judd, K.3
  • 50
    • 0001351751 scopus 로고    scopus 로고
    • Nonlinear deterministic forecasting of daily dollar exchange rates
    • Cao L., Soofi A. S., Nonlinear deterministic forecasting of daily dollar exchange rates International Journal of Forecasting 1999 15 4 421 430
    • (1999) International Journal of Forecasting , vol.15 , Issue.4 , pp. 421-430
    • Cao, L.1    Soofi, A.S.2
  • 51
    • 0003645482 scopus 로고    scopus 로고
    • Nonlinear signal processing using neural networks: prediction and system modelling
    • Los Alamos Report LA-UR 872662, 1887
    • Lapedes A., Farber R., Nonlinear signal processing using neural networks: prediction and system modelling. submitted to Proceedings of the IEEE, Los Alamos Report LA-UR 872662, 1887
    • Proceedings of the IEEE
    • Lapedes, A.1    Farber, R.2
  • 53
    • 0034381189 scopus 로고    scopus 로고
    • Predicting chaotic time series using recurrent neural network
    • Zhang J.-S., Xiao X.-C., Predicting chaotic time series using recurrent neural network Chinese Physics Letters 2000 17 2 88 90
    • (2000) Chinese Physics Letters , vol.17 , Issue.2 , pp. 88-90
    • Zhang, J.-S.1    Xiao, X.-C.2
  • 54
    • 0035586471 scopus 로고    scopus 로고
    • Predicting hyper-chaotic time series using adaptive higher-order nonlinear filter
    • Zhang J.-S., Xiao X.-C., Predicting hyper-chaotic time series using adaptive higher-order nonlinear filter Chinese Physics Letters 2001 18 3 337 340
    • (2001) Chinese Physics Letters , vol.18 , Issue.3 , pp. 337-340
    • Zhang, J.-S.1    Xiao, X.-C.2
  • 55
    • 0000095965 scopus 로고
    • Reconstructing equations of motion from experimental data with unobserved variables
    • Breeden J. L., Hbler A., Reconstructing equations of motion from experimental data with unobserved variables Physical Review A 1990 42 10 5817 5826
    • (1990) Physical Review A , vol.42 , Issue.10 , pp. 5817-5826
    • Breeden, J.L.1    Hbler, A.2
  • 56
    • 0010465428 scopus 로고
    • Noise in the modeling and control of dynamical systems
    • Breeden J. L., Dinkelacker F., Hbler A., Noise in the modeling and control of dynamical systems Physical Review A 1990 42 10 5827 5836
    • (1990) Physical Review A , vol.42 , Issue.10 , pp. 5827-5836
    • Breeden, J.L.1    Dinkelacker, F.2    Hbler, A.3
  • 57
    • 0000130270 scopus 로고
    • Reconstruction of the vector fields of continuous dynamical systems from numerical scalar time series
    • Gouesbet G., Reconstruction of the vector fields of continuous dynamical systems from numerical scalar time series Physical Review A 1991 43 10 5321 5331
    • (1991) Physical Review A , vol.43 , Issue.10 , pp. 5321-5331
    • Gouesbet, G.1
  • 58
    • 0000404649 scopus 로고
    • Reconstruction of vector fields: the case of the Lorenz system
    • Gouesbet G., Reconstruction of vector fields: the case of the Lorenz system Physical Review A 1992 46 4 1784 1796
    • (1992) Physical Review A , vol.46 , Issue.4 , pp. 1784-1796
    • Gouesbet, G.1
  • 59
    • 0001600637 scopus 로고
    • Construction of phenomenological models from numerical scalar time series
    • Gouesbet G., Maquet J., Construction of phenomenological models from numerical scalar time series Physica D 1992 58 14 202 215
    • (1992) Physica D , vol.58 , Issue.14 , pp. 202-215
    • Gouesbet, G.1    Maquet, J.2
  • 60
    • 0000557232 scopus 로고
    • Global vector-field reconstruction by using a multivariate polynomial L 2 approximation on nets
    • Gouesbet G., Letellier C., Global vector-field reconstruction by using a multivariate polynomial L 2 approximation on nets Physical Review E 1994 49 6 4955 4972
    • (1994) Physical Review E , vol.49 , Issue.6 , pp. 4955-4972
    • Gouesbet, G.1    Letellier, C.2
  • 61
    • 0001727086 scopus 로고
    • Functional reconstruction and local prediction of chaotic time series
    • Giona M., Lentini F., Cimagalli V., Functional reconstruction and local prediction of chaotic time series Physical Review A 1991 44 6 3496 3502
    • (1991) Physical Review A , vol.44 , Issue.6 , pp. 3496-3502
    • Giona, M.1    Lentini, F.2    Cimagalli, V.3
  • 62
    • 0001581120 scopus 로고
    • Modeling and synchronizing chaotic systems from time-series data
    • Brown R., Rulkov N. F., Tracy E. R., Modeling and synchronizing chaotic systems from time-series data Physical Review E 1994 49 5 3784 3800
    • (1994) Physical Review E , vol.49 , Issue.5 , pp. 3784-3800
    • Brown, R.1    Rulkov, N.F.2    Tracy, E.R.3
  • 64
    • 0035888224 scopus 로고    scopus 로고
    • Structure-selection techniques applied to continuous-time nonlinear models
    • DOI 10.1016/S0167-2789(01)00313-X, PII S016727890100313X
    • Aguirre L. A., Freitas U. S., Letellier C., Maquet J., Structure-selection techniques applied to continuous-time nonlinear models Physica D 2001 158 14 1 18 (Pubitemid 32903826)
    • (2001) Physica D: Nonlinear Phenomena , vol.158 , Issue.1-4 , pp. 1-18
    • Aguirre, L.A.1    Freitas, U.S.2    Letellier, C.3    Maquet, J.4
  • 65
    • 4244045020 scopus 로고    scopus 로고
    • Constructing nonautonomous differential equations from experimental time series
    • Bezruchko B. P., Smirnov D. A., Constructing nonautonomous differential equations from experimental time series Physical Review E 2000 63 1 7
    • (2000) Physical Review E , vol.63 , Issue.1 , pp. 7
    • Bezruchko, B.P.1    Smirnov, D.A.2
  • 66
    • 84983708323 scopus 로고    scopus 로고
    • Ansatz library for global modeling with a structure selection
    • Lainscsek C. S. M., Letellier C., Schrrer F., Ansatz library for global modeling with a structure selection Physical Review E 2001 64 1 15
    • (2001) Physical Review E , vol.64 , Issue.1 , pp. 15
    • Lainscsek, C.S.M.1    Letellier, C.2    Schrrer, F.3
  • 69
    • 0000005427 scopus 로고
    • Global vector field reconstruction from a chaotic experimental signal in copper electrodissolution
    • Letellier C., Le Sceller L., Marchal E., Global vector field reconstruction from a chaotic experimental signal in copper electrodissolution Physical Review E 1995 51 5 4262 4266
    • (1995) Physical Review E , vol.51 , Issue.5 , pp. 4262-4266
    • Letellier, C.1    Le Sceller, L.2    Marchal, E.3
  • 70
    • 0002564289 scopus 로고    scopus 로고
    • Determining mixed linear-nonlinear coupled differential equations from multivariate discrete time series sequences
    • PII S0167278996002485
    • Irving A. D., Dewson T., Determining mixed linear-nonlinear coupled differential equations from multivariate discrete time series sequences Physica D 1997 102 1-2 15 36 (Pubitemid 127701372)
    • (1997) Physica D: Nonlinear Phenomena , vol.102 , Issue.1-2 , pp. 15-36
    • Irving, A.D.1    Dewson, T.2
  • 72
  • 73
    • 0034683569 scopus 로고    scopus 로고
    • Parametric, nonparametric and parametric modelling of a chaotic circuit time series
    • Timmer J., Rust H., Horbelt W., Voss H. U., Parametric, nonparametric and parametric modelling of a chaotic circuit time series Physics Letters A 2000 274 3-4 123 134
    • (2000) Physics Letters A , vol.274 , Issue.34 , pp. 123-134
    • Timmer, J.1    Rust, H.2    Horbelt, W.3    Voss, H.U.4
  • 74
    • 4244071806 scopus 로고    scopus 로고
    • Identifying physical properties of a CO 2 laser by dynamical modeling of measured time series
    • Horbelt W., Timmer J., Bnner M. J., Meucci R., Ciofini M., Identifying physical properties of a CO 2 laser by dynamical modeling of measured time series Physical Review E 2001 64 1 7
    • (2001) Physical Review E , vol.64 , Issue.1 , pp. 7
    • Horbelt, W.1    Timmer, J.2    Bnner, M.J.3    Meucci, R.4    Ciofini, M.5
  • 75
    • 0031106678 scopus 로고    scopus 로고
    • Linear and nonlinear ARMA model parameter estimation using an artificial neural network
    • Chon K. H., Cohen R. J., Linear and nonlinear ARMA model parameter estimation using an artificial neural network IEEE Transactions on Biomedical Engineering 1997 44 3 168 174
    • (1997) IEEE Transactions on Biomedical Engineering , vol.44 , Issue.3 , pp. 168-174
    • Chon, K.H.1    Cohen, R.J.2
  • 77
    • 35448986904 scopus 로고    scopus 로고
    • Building dynamical models from data and prior knowledge: the case of the first period-doubling bifurcation
    • Aguirre L. A., Furtado E. C., Building dynamical models from data and prior knowledge: the case of the first period-doubling bifurcation Physical Review E 2007 76 4 13
    • (2007) Physical Review E , vol.76 , Issue.4 , pp. 13
    • Aguirre, L.A.1    Furtado, E.C.2
  • 79
    • 0000437940 scopus 로고
    • Predicting time series using a neural network as a method of distinguishing chaos from noise
    • Elsner J. B., Predicting time series using a neural network as a method of distinguishing chaos from noise Journal of Physics A 1992 25 4 843 850
    • (1992) Journal of Physics A , vol.25 , Issue.4 , pp. 843-850
    • Elsner, J.B.1
  • 82
    • 0032446982 scopus 로고    scopus 로고
    • A bifurcation study on neural network models for nonlinear dynamic systems
    • Henrique H. M., Lima E. L., Pinto J. C., A bifurcation study on neural network models for nonlinear dynamic systems Latin American Applied Research 1998 28 3 187 200 (Pubitemid 128337189)
    • (1998) Latin American Applied Research , vol.28 , Issue.3 , pp. 187-200
    • Henrique, H.M.1    Lima, E.L.2    Pinto, J.C.3
  • 84
    • 0000809163 scopus 로고    scopus 로고
    • Nonlinear modelling and prediction with feedforward and recurrent networks
    • PII S0167278997000328
    • Genay R., Liu T., Nonlinear modeling and prediction with feedforward and recurrent networks Physica D 1997 108 1-2 119 134 (Pubitemid 127701552)
    • (1997) Physica D: Nonlinear Phenomena , vol.108 , Issue.1-2 , pp. 119-134
    • Gencay, R.1    Liu, T.2
  • 85
    • 0035452859 scopus 로고    scopus 로고
    • Extraction of nonlinear dynamics from short and noisy time series
    • DOI 10.1016/S0960-0779(00)00163-6, PII S0960077900001636
    • Boudjema G., Cazelles B., Extraction of nonlinear dynamics from short and noisy time series Chaos, Solitons Fractals 2001 12 11 2051 2069 (Pubitemid 32518180)
    • (2001) Chaos, Solitons and Fractals , vol.12 , Issue.11 , pp. 2051-2069
    • Boudjema, G.1    Cazelles, B.2
  • 86
    • 0035619587 scopus 로고    scopus 로고
    • A method of model validation for chaotic chemical reaction systems based on neural networks
    • Kim H. J., Chang K. S., A method of model validation for chaotic chemical reaction systems based on neural networks Korean Journal of Chemical Engineering 2001 18 5 623 629
    • (2001) Korean Journal of Chemical Engineering , vol.18 , Issue.5 , pp. 623-629
    • Kim, H.J.1    Chang, K.S.2
  • 87
    • 33746630356 scopus 로고    scopus 로고
    • Hackensack, NJ, USA World Scientific World Scientific Series on Nonlinear Science. Series A
    • Small M., Applied Nonlinear Time Series Analysis 2005 52 Hackensack, NJ, USA World Scientific xiv+245 World Scientific Series on Nonlinear Science. Series A
    • (2005) Applied Nonlinear Time Series Analysis , vol.52 , pp. 245
    • Small, M.1
  • 88
    • 0001977937 scopus 로고
    • Identification and prediction of low-dimensional dynamics
    • Smith L. A., Identification and prediction of low-dimensional dynamics Physica D 1992 58 14 50 76
    • (1992) Physica D , vol.58 , Issue.14 , pp. 50-76
    • Smith, L.A.1
  • 90
    • 0346057281 scopus 로고    scopus 로고
    • Time series analysis and prediction on complex dynamical behavior observed in a blast furnace
    • Miyano T., Kimoto S., Shibuta H., Nakashima K., Ikenaga Y., Aihara K., Time series analysis and prediction on complex dynamical behavior observed in a blast furnace Physica D 2000 135 3-4 305 330
    • (2000) Physica D , vol.135 , Issue.34 , pp. 305-330
    • Miyano, T.1    Kimoto, S.2    Shibuta, H.3    Nakashima, K.4    Ikenaga, Y.5    Aihara, K.6
  • 91
    • 0036722553 scopus 로고    scopus 로고
    • Modelling the dynamics of nonlinear time series using canonical variate analysis
    • DOI 10.1016/S0167-2789(02)00534-1, PII S0167278902005341
    • Pilgram B., Judd K., Mees A., Modelling the dynamics of nonlinear time series using canonical variate analysis Physica D 2002 170 2 103 117 (Pubitemid 34813923)
    • (2002) Physica D: Nonlinear Phenomena , vol.170 , Issue.2 , pp. 103-117
    • Pilgram, B.1    Judd, K.2    Mees, A.3
  • 92
    • 0342474427 scopus 로고    scopus 로고
    • Generalized one-parameter bifurcation diagram reconstruction using time series
    • PII S0167278998002000
    • Bagarinao E. Jr., Nomura T., Pakdaman K., Sato S., Generalized one-parameter bifurcation diagram reconstruction using time series Physica D 1998 124 13 258 270 (Pubitemid 128636790)
    • (1998) Physica D: Nonlinear Phenomena , vol.124 , Issue.1-3 , pp. 258-270
    • Bagarinao Jr., E.1    Nomura, T.2    Pakdaman, K.3    Sato, S.4
  • 95
    • 0033932475 scopus 로고    scopus 로고
    • Reconstructing bifurcation diagrams of dynamical systems using measured time series
    • Bagarinao E. Jr., Pakdaman K., Nomura T., Sato S., Reconstructing bifurcation diagrams of dynamical systems using measured time series Methods of Information in Medicine 2000 39 2 146 149 (Pubitemid 30423300)
    • (2000) Methods of Information in Medicine , vol.39 , Issue.2 , pp. 146-149
    • Bagarinao, E.1    Pakdaman, K.2    Nomura, T.3    Sato, S.4
  • 96
    • 0000510147 scopus 로고    scopus 로고
    • Detection of nonlinear dynamics in short, noisy time series
    • Barahona M., Poon C.-S., Detection of nonlinear dynamics in short, noisy time series Nature 1996 381 6579 215 217 (Pubitemid 126557440)
    • (1996) Nature , vol.381 , Issue.6579 , pp. 215-217
    • Barahona, M.1    Poon, C.-S.2
  • 98
    • 27244459586 scopus 로고    scopus 로고
    • Using data-driven discrete-time models and the unscented Kalman filter to estimate unobserved variables of nonlinear systems
    • Aguirre L. A., Teixeira B. O. S., Trres L. A. B., Using data-driven discrete-time models and the unscented Kalman filter to estimate unobserved variables of nonlinear systems Physical Review E 2005 72 2 12
    • (2005) Physical Review E , vol.72 , Issue.2 , pp. 12
    • Aguirre, L.A.1    Teixeira, B.O.S.2    Trres, L.A.B.3
  • 102
    • 46449112473 scopus 로고    scopus 로고
    • Testing for intracycle determinism in pseudoperiodic time series
    • Coelho M. C. S., Mendes E. M. A. M., Aguirre L. A., Testing for intracycle determinism in pseudoperiodic time series Chaos 2008 18 2 12
    • (2008) Chaos , vol.18 , Issue.2 , pp. 12
    • Coelho, M.C.S.1    Mendes, E.M.A.M.2    Aguirre, L.A.3
  • 103
    • 35348835899 scopus 로고    scopus 로고
    • The influence of noise on nonlinear time series detection based on Volterra-Wiener-Korenberg model
    • DOI 10.1016/j.chaos.2006.06.084, PII S0960077906006801
    • Lei M., Meng G., The influence of noise on nonlinear time series detection based on Volterra-Wiener-Korenberg model Chaos, Solitons Fractals 2008 36 2 512 516 (Pubitemid 47588912)
    • (2008) Chaos, Solitons and Fractals , vol.36 , Issue.2 , pp. 512-516
    • Lei, M.1    Meng, G.2
  • 104
    • 0034355220 scopus 로고    scopus 로고
    • Nonlinear interactions in a rotating disk flow: from a Volterra model to the Ginzburg-Landau equation
    • Floriani E., Dudok de Wit T., Le Gal P., Nonlinear interactions in a rotating disk flow: from a Volterra model to the Ginzburg-Landau equation Chaos 2000 10 4 834 847
    • (2000) Chaos , vol.10 , Issue.4 , pp. 834-847
    • Floriani, E.1    Dudok De Wit, T.2    Le Gal, P.3
  • 106
    • 42449104286 scopus 로고    scopus 로고
    • Forecasting the time series of sunspot numbers
    • Aguirre L. A., Letellier C., Maquet J., Forecasting the time series of sunspot numbers Solar Physics 2008 249 1 103 120
    • (2008) Solar Physics , vol.249 , Issue.1 , pp. 103-120
    • Aguirre, L.A.1    Letellier, C.2    Maquet, J.3
  • 107
    • 0024628610 scopus 로고
    • Identification of nonlinear rational systems using a prediction-error estimation algorithm
    • Billings S. A., Chen S., Identification of nonlinear rational systems using a prediction-error estimation algorithm International Journal of Systems Science 1989 20 3 467 494
    • (1989) International Journal of Systems Science , vol.20 , Issue.3 , pp. 467-494
    • Billings, S.A.1    Chen, S.2
  • 108
    • 0003107035 scopus 로고
    • Recursive parameter estimation for nonlinear rational models
    • Zhu Q. M., Billings S. A., Recursive parameter estimation for nonlinear rational models Journal of Systems Engineering 1991 1 63 76
    • (1991) Journal of Systems Engineering , vol.1 , pp. 63-76
    • Zhu, Q.M.1    Billings, S.A.2
  • 109
    • 0000065875 scopus 로고
    • Parameter estimation for stochastic nonlinear rational models
    • Zhu Q. M., Billings S. A., Parameter estimation for stochastic nonlinear rational models International Journal of Control 1993 57 2 309 333
    • (1993) International Journal of Control , vol.57 , Issue.2 , pp. 309-333
    • Zhu, Q.M.1    Billings, S.A.2
  • 114
    • 5444260192 scopus 로고    scopus 로고
    • Identification and reconstruction of chaotic systems using multiresolution wavelet decompositions
    • Wei H. L., Billings S. A., Identification and reconstruction of chaotic systems using multiresolution wavelet decompositions International Journal of Systems Science 2004 35 9 511 526
    • (2004) International Journal of Systems Science , vol.35 , Issue.9 , pp. 511-526
    • Wei, H.L.1    Billings, S.A.2
  • 115
    • 0142209526 scopus 로고    scopus 로고
    • A relational approach for complex system identification
    • Campello R. J. G. B., do Amaral W. C., A relational approach for complex system identification Controle Automao 1999 10 3 139 148
    • (1999) Controle Automao , vol.10 , Issue.3 , pp. 139-148
    • Campello, R.J.G.B.1    Do Amaral, W.C.2
  • 116
    • 0033116173 scopus 로고    scopus 로고
    • Stabilizing controller design for uncertain nonlinear systems using fuzzy models
    • Teixeira M. C. M., Zak S. H., Stabilizing controller design for uncertain nonlinear systems using fuzzy models IEEE Transactions on Fuzzy Systems 1999 7 2 133 142
    • (1999) IEEE Transactions on Fuzzy Systems , vol.7 , Issue.2 , pp. 133-142
    • Teixeira, M.C.M.1    Zak, S.H.2
  • 117
    • 0035360372 scopus 로고    scopus 로고
    • Designing fuzzy inference systems from data: an interpretability-oriented review
    • Guillaume S., Designing fuzzy inference systems from data: an interpretability-oriented review IEEE Transactions on Fuzzy Systems 2001 9 3 426 443
    • (2001) IEEE Transactions on Fuzzy Systems , vol.9 , Issue.3 , pp. 426-443
    • Guillaume, S.1
  • 118
    • 0142027067 scopus 로고    scopus 로고
    • Heuristic learning in recurrent neural fuzzy networks
    • Ballini R., Gomide F., Heuristic learning in recurrent neural fuzzy networks Journal of Intelligent Fuzzy Systems 2002 13 24 63 74
    • (2002) Journal of Intelligent Fuzzy Systems , vol.13 , Issue.24 , pp. 63-74
    • Ballini, R.1    Gomide, F.2
  • 119
    • 0028544274 scopus 로고
    • An adaptive fuzzy system for modeling chaos
    • Hiew H. L., Tsang C. P., An adaptive fuzzy system for modeling chaos Information Sciences 1994 81 3-4 193 212
    • (1994) Information Sciences , vol.81 , Issue.34 , pp. 193-212
    • Hiew, H.L.1    Tsang, C.P.2
  • 120
    • 34047174524 scopus 로고    scopus 로고
    • Computational intelligence approaches and linear models in case studies of forecasting exchange rates
    • DOI 10.1016/j.eswa.2006.07.008, PII S0957417406002144
    • Santos A. A. P., da Costa N. C. A. Jr., dos Santos Coelho L., Computational intelligence approaches and linear models in case studies of forecasting exchange rates Expert Systems with Applications 2007 33 4 816 823 (Pubitemid 46509581)
    • (2007) Expert Systems with Applications , vol.33 , Issue.4 , pp. 816-823
    • Santos, A.A.P.1    Da Costa Jr., N.C.A.2    Dos Santos Coelho, L.3
  • 122
    • 0000948742 scopus 로고
    • A dynamical systems approach to modeling input-output systems
    • New York, NY, USA Addison Wesley
    • Casdagli M., Casdagli M., Eubank S., A dynamical systems approach to modeling input-output systems Nonlinear Modeling and Forecasting 1992 New York, NY, USA Addison Wesley 265 281
    • (1992) Nonlinear Modeling and Forecasting , pp. 265-281
    • Casdagli, M.1    Casdagli, M.2    Eubank, S.3
  • 123
    • 0039939886 scopus 로고
    • Application of nonlinear time-series models to driven systems
    • New York, NY, USA Addison Wesley
    • Hunter N. F., Casdagli M., Eubank S., Application of nonlinear time-series models to driven systems Nonlinear Modeling and Forecasting 1992 New York, NY, USA Addison Wesley 467 491
    • (1992) Nonlinear Modeling and Forecasting , pp. 467-491
    • Hunter, N.F.1    Casdagli, M.2    Eubank, S.3
  • 124
    • 0022011031 scopus 로고
    • INPUT-OUTPUT PARAMETRIC MODELS FOR NON-LINEAR SYSTEMS. PART I: DETERMINISTIC NON-LINEAR SYSTEMS.
    • Leontaritis I. J., Billings S. A., Input-output parametric models for nonlinear systemspart I: deterministic non-linear systems International Journal of Control 1985 41 2 303 328 (Pubitemid 15476363)
    • (1985) International Journal of Control , vol.41 , Issue.2 , pp. 303-328
    • Leontaritis, I.J.1    Billings, S.A.2
  • 126
    • 0344465025 scopus 로고    scopus 로고
    • Reconstruction of the Lorenz and Chen systems with noisy observations
    • Lu J., L J., Xie J., Chen G., Reconstruction of the Lorenz and Chen systems with noisy observations Computers Mathematics with Applications 2003 46 8-9 1427 1434
    • (2003) Computers Mathematics with Applications , vol.46 , Issue.89 , pp. 1427-1434
    • Lu, J.1    Xie, J.2    Chen, G.3
  • 127
    • 0036489678 scopus 로고    scopus 로고
    • A note on discretization of nonlinear differential equations
    • Mendes E. M. A. M., Billings S. A., A note on discretization of nonlinear differential equations Chaos 2002 12 1 66 71
    • (2002) Chaos , vol.12 , Issue.1 , pp. 66-71
    • Mendes, E.M.A.M.1    Billings, S.A.2
  • 128
    • 0842285886 scopus 로고    scopus 로고
    • Displacement in the parameter space versus spurious solution of discretization with large time step
    • DOI 10.1088/0305-4470/37/4/008, PII S0305447004637152
    • Mendes E. M. A. M., Letellier C., Displacement in the parameter space versus spurious solution of discretization with large time step Journal of Physics A 2004 37 4 1203 1218 (Pubitemid 38178225)
    • (2004) Journal of Physics A: Mathematical and General , vol.37 , Issue.4 , pp. 1203-1218
    • Mendes, E.1    Letellier, C.2
  • 130
    • 0031171247 scopus 로고    scopus 로고
    • Discrete time recurrent neural network architectures: A unifying review
    • DOI 10.1016/S0925-2312(97)00161-6, PII S09252312970001617
    • Tsoia A. C., Back A., Discrete time recurrent neural network architectures: a unifying review Neurocomputing 1997 15 3-4 183 223 (Pubitemid 27301516)
    • (1997) Neurocomputing , vol.15 , Issue.3-4 , pp. 183-223
    • Tsoia, A.C.1    Back, A.2
  • 131
    • 0034331142 scopus 로고    scopus 로고
    • Improving generalization of MLPs with multi-objective optimization
    • DOI 10.1016/S0925-2312(00)00327-1, PII S0925231200003271
    • de Albuquerque Teixeira R., Braga A. P., Takahashi R. H. C., Saldanha R. R., Improving generalization of MLPs with multi-objective optimization Neurocomputing 2000 35 14 189 194 (Pubitemid 30831059)
    • (2000) Neurocomputing , vol.35 , pp. 189-194
    • De Albuquerque Teixeira, R.1    Braga, A.P.2    Takahashi, R.H.C.3    Saldanha, R.R.4
  • 132
    • 41349101486 scopus 로고    scopus 로고
    • Minimum description length neural networks for time series prediction
    • Small M., Tse C. K., Minimum description length neural networks for time series prediction Physical Review E 2002 66 6 12
    • (2002) Physical Review E , vol.66 , Issue.6 , pp. 12
    • Small, M.1    Tse, C.K.2
  • 133
    • 34249073096 scopus 로고    scopus 로고
    • Controlling the parallel layer perceptron complexity using a multiobjective learning algorithm
    • Vieira D. A. G., Vasconcelos J. A., Caminhas W. M., Controlling the parallel layer perceptron complexity using a multiobjective learning algorithm Neural Computing Applications 2007 16 4-5 317 325
    • (2007) Neural Computing Applications , vol.16 , Issue.45 , pp. 317-325
    • Vieira, D.A.G.1    Vasconcelos, J.A.2    Caminhas, W.M.3
  • 134
    • 1842865087 scopus 로고    scopus 로고
    • Model order selection of nonlinear input-output modelsa clustering based approach
    • Feil B., Abonyi J., Szeifert F., Model order selection of nonlinear input-output modelsa clustering based approach Journal of Process Control 2004 14 6 593 602
    • (2004) Journal of Process Control , vol.14 , Issue.6 , pp. 593-602
    • Feil, B.1    Abonyi, J.2    Szeifert, F.3
  • 135
    • 19844362946 scopus 로고    scopus 로고
    • Genetic programming for the identification of nonlinear input-output models
    • DOI 10.1021/ie049626e
    • Madr J., Abonyi J., Szeifert F., Genetic programming for the identification of nonlinear input-output models Industrial and Engineering Chemistry Research 2005 44 9 3178 3186 (Pubitemid 40763447)
    • (2005) Industrial and Engineering Chemistry Research , vol.44 , Issue.9 , pp. 3178-3186
    • Madar, J.1    Abonyi, J.2    Szeifert, F.3
  • 136
    • 35949005876 scopus 로고
    • Fitting ordinary differential equations to chaotic data
    • Baake E., Baake M., Bock H. G., Briggs K. M., Fitting ordinary differential equations to chaotic data Physical Review A 1992 45 8 5524 5529
    • (1992) Physical Review A , vol.45 , Issue.8 , pp. 5524-5529
    • Baake, E.1    Baake, M.2    Bock, H.G.3    Briggs, K.M.4
  • 137
    • 0001976684 scopus 로고    scopus 로고
    • Inverting chaos: extracting system parameters from experimental data
    • Baker G. L., Gollub J. P., Blackburn J. A., Inverting chaos: extracting system parameters from experimental data Chaos 1996 6 4 528 533
    • (1996) Chaos , vol.6 , Issue.4 , pp. 528-533
    • Baker, G.L.1    Gollub, J.P.2    Blackburn, J.A.3
  • 138
    • 0032131356 scopus 로고    scopus 로고
    • Global Reconstruction in the Presence of a priori Information
    • PII S0960077998000617
    • Anishchenko V. S., Pavlov A. N., Janson N. B., Global reconstruction in the presence of a priori information Chaos, Solitons Fractals 1998 9 8 1267 1278 (Pubitemid 128435192)
    • (1998) Chaos, Solitons and Fractals , vol.9 , Issue.8 , pp. 1267-1278
    • Anishchenko, V.S.1    Pavlov, A.N.2    Janson, N.B.3
  • 139
    • 0000383336 scopus 로고
    • Extraction of dynamical equations from chaotic data
    • Rowlands G., Sprott J. C., Extraction of dynamical equations from chaotic data Physica D 1992 58 14 251 259
    • (1992) Physica D , vol.58 , Issue.14 , pp. 251-259
    • Rowlands, G.1    Sprott, J.C.2
  • 141
  • 142
    • 0002888015 scopus 로고
    • Dynamical effects of overparametrization in nonlinear models
    • Aguirre L. A., Billings S. A., Dynamical effects of overparametrization in nonlinear models Physica D 1995 80 1-2 26 40
    • (1995) Physica D , vol.80 , Issue.12 , pp. 26-40
    • Aguirre, L.A.1    Billings, S.A.2
  • 144
    • 0039862370 scopus 로고    scopus 로고
    • Global nonlinear polynomial models: structure, term clusters and fixed points
    • Aguirre L. A., Mendes E. M. A. M., Global nonlinear polynomial models: structure, term clusters and fixed points International Journal of Bifurcation and Chaos 1996 6 2 279 294
    • (1996) International Journal of Bifurcation and Chaos , vol.6 , Issue.2 , pp. 279-294
    • Aguirre, L.A.1    Mendes, E.M.A.M.2
  • 148
    • 4243352651 scopus 로고
    • Some remarks on structure selection for nonlinear models
    • Aguirre L. A., Some remarks on structure selection for nonlinear models International Journal of Bifurcation and Chaos 1994 4 6 1707 1714
    • (1994) International Journal of Bifurcation and Chaos , vol.4 , Issue.6 , pp. 1707-1714
    • Aguirre, L.A.1
  • 149
    • 0029373832 scopus 로고
    • Improved structure selection for nonlinear models based on term clustering
    • Aguirre L. A., Billings S. A., Improved structure selection for nonlinear models based on term clustering International Journal of Control 1995 62 3 569 587
    • (1995) International Journal of Control , vol.62 , Issue.3 , pp. 569-587
    • Aguirre, L.A.1    Billings, S.A.2
  • 150
    • 0009269810 scopus 로고    scopus 로고
    • Parameter uncertainties in models of equivariant dynamical systems
    • PII S0167278996001789
    • Brown R., In V., Tracy E. R., Parameter uncertainties in models of equivariant dynamical systems Physica D 1997 102 3-4 208 226 (Pubitemid 127701384)
    • (1997) Physica D: Nonlinear Phenomena , vol.102 , Issue.3-4 , pp. 208-226
    • Brown, R.1    In, V.2    Tracy, E.R.3
  • 151
    • 42749105486 scopus 로고    scopus 로고
    • Constraining the topology of neural networks to ensure dynamics with symmetry properties
    • Aguirre L. A., Lopes R. A. M., Amaral G. F. V., Letellier C., Constraining the topology of neural networks to ensure dynamics with symmetry properties Physical Review E 2004 69 2 11
    • (2004) Physical Review E , vol.69 , Issue.2 , pp. 11
    • Aguirre, L.A.1    Lopes, R.A.M.2    Amaral, G.F.V.3    Letellier, C.4
  • 152
    • 0032187521 scopus 로고    scopus 로고
    • Determination of model order for NARX models directly from input-output data
    • PII S0959152498000134
    • Bomberger J. D., Seborg D. E., Determination of model order for NARX models directly from input-output data Journal of Process Control 1998 8 5-6 459 468 (Pubitemid 128400784)
    • (1998) Journal of Process Control , vol.8 , Issue.5-6 , pp. 459-468
    • Bomberger, J.D.1    Seborg, D.E.2
  • 154
    • 0001263962 scopus 로고
    • On selecting models for nonlinear time series
    • Judd K., Mees A., On selecting models for nonlinear time series Physica D 1995 82 4 426 444
    • (1995) Physica D , vol.82 , Issue.4 , pp. 426-444
    • Judd, K.1    Mees, A.2
  • 155
    • 0024685547 scopus 로고
    • Identification of MIMO non-linear systems using a forward-regression orthogonal estimator
    • Billings S. A., Chen S., Korenberg M. J., Identification of MIMO nonlinear systems using a forward-regression orthogonal estimator International Journal of Control 1989 49 6 2157 2189 (Pubitemid 20610944)
    • (1989) International Journal of Control , vol.49 , Issue.6 , pp. 2157-2189
    • Billings, S.A.1    Chen, S.2    Korenberg, M.J.3
  • 156
    • 58149208723 scopus 로고
    • Identification of models for chaotic systems from noisy data: implications for performance and nonlinear filtering
    • Aguirre L. A., Billings S. A., Identification of models for chaotic systems from noisy data: implications for performance and nonlinear filtering Physica D 1995 85 1-2 239 258
    • (1995) Physica D , vol.85 , Issue.12 , pp. 239-258
    • Aguirre, L.A.1    Billings, S.A.2
  • 158
    • 0036710131 scopus 로고    scopus 로고
    • Investigating nonlinear dynamics from time series: the influence of symmetries and the choice of observables
    • Letellier C., Aguirre L. A., Investigating nonlinear dynamics from time series: the influence of symmetries and the choice of observables Chaos 2002 12 3 549 558
    • (2002) Chaos , vol.12 , Issue.3 , pp. 549-558
    • Letellier, C.1    Aguirre, L.A.2
  • 159
    • 28444439205 scopus 로고    scopus 로고
    • How the choice of the observable may influence the analysis of nonlinear dynamical systems
    • DOI 10.1016/j.cnsns.2005.01.003, PII S1007570405000262
    • Letellier C., Aguirre L. A., Maquet J., How the choice of the observable may influence the analysis of nonlinear dynamical systems Communications in Nonlinear Science and Numerical Simulation 2006 11 5 555 576 (Pubitemid 41722799)
    • (2006) Communications in Nonlinear Science and Numerical Simulation , vol.11 , Issue.5 , pp. 555-576
    • Letellier, C.1    Aguirre, L.2    Maquet, J.3
  • 161
    • 41349102509 scopus 로고    scopus 로고
    • Choice of dynamical variables for global reconstruction of model equations from time series
    • Smirnov D. A., Bezruchko B. P., Seleznev Y. P., Choice of dynamical variables for global reconstruction of model equations from time series Physical Review E 2002 65 2 7
    • (2002) Physical Review E , vol.65 , Issue.2 , pp. 7
    • Smirnov, D.A.1    Bezruchko, B.P.2    Seleznev, Y.P.3
  • 162
    • 0000497870 scopus 로고    scopus 로고
    • Embedding as a modeling problem
    • PII S016727899800089X
    • Judd K., Mees A., Embedding as a modeling problem Physica D 1998 120 3-4 273 286 (Pubitemid 128676680)
    • (1998) Physica D: Nonlinear Phenomena , vol.120 , Issue.3-4 , pp. 273-286
    • Judd, K.1    Mees, A.2
  • 163
    • 0000186307 scopus 로고    scopus 로고
    • Estimating model parameters from time series by autosynchronization
    • Parlitz U., Estimating model parameters from time series by autosynchronization Physical Review Letters 1996 76 8 1232 1235 (Pubitemid 126586086)
    • (1996) Physical Review Letters , vol.76 , Issue.8 , pp. 1232-1235
    • Parlitz, U.1
  • 165
    • 7044223126 scopus 로고    scopus 로고
    • Fitting model equations to time series using chaos synchronization
    • Tao C., Zhang Y., Du G., Jiang J. J., Fitting model equations to time series using chaos synchronization Physics Letters A 2004 332 3-4 197 206
    • (2004) Physics Letters A , vol.332 , Issue.34 , pp. 197-206
    • Tao, C.1    Zhang, Y.2    Du, G.3    Jiang, J.J.4
  • 166
    • 41349090048 scopus 로고    scopus 로고
    • Using geometric control and chaotic synchronization to estimate an unknown model parameter
    • Freitas U. S., Macau E. E. N., Grebogi C., Using geometric control and chaotic synchronization to estimate an unknown model parameter Physical Review E 2005 71 4 4
    • (2005) Physical Review E , vol.71 , Issue.4 , pp. 4
    • Freitas, U.S.1    Macau, E.E.N.2    Grebogi, C.3
  • 167
    • 0001341233 scopus 로고
    • Problems in estimating dynamics from data
    • Kostelich E. J., Problems in estimating dynamics from data Physica D 1992 58 14 138 152
    • (1992) Physica D , vol.58 , Issue.14 , pp. 138-152
    • Kostelich, E.J.1
  • 168
    • 0001128249 scopus 로고    scopus 로고
    • Unbiased reconstruction of the dynamics underlying a noisy chaotic time series
    • Jaeger L., Kantz H., Unbiased reconstruction of the dynamics underlying a noisy chaotic time series Chaos 1996 6 3 440 450
    • (1996) Chaos , vol.6 , Issue.3 , pp. 440-450
    • Jaeger, L.1    Kantz, H.2
  • 170
    • 22244457392 scopus 로고    scopus 로고
    • Parameter identification in noisy extended systems: A hydrodynamic case
    • PII S0167278996002862
    • Fullana J. M., Rossi M., Zaleski S., Parameter identification in noisy extended systems: a hydrodynamic case Physica D 1997 103 14 564 575 (Pubitemid 127701435)
    • (1997) Physica D: Nonlinear Phenomena , vol.103 , Issue.1-4 , pp. 564-575
    • Fullana, J.M.1    Rossi, M.2    Zaleski, S.3
  • 171
    • 0034276175 scopus 로고    scopus 로고
    • On the trajectory method for the reconstruction of differential equations from time series
    • DOI 10.1023/A:1008335507636
    • Perona P., Porporato A., Ridolfi L., On the trajectory method for the reconstruction of differential equations from time series Nonlinear Dynamics 2000 23 1 13 33 (Pubitemid 30924537)
    • (2000) Nonlinear Dynamics , vol.23 , Issue.1 , pp. 13-33
    • Perona, P.1    Porporato, A.2    Ridoefi, E.3
  • 172
    • 33845987405 scopus 로고    scopus 로고
    • Prediction- and simulation-error based perceptron training: Solution space analysis and a novel combined training scheme
    • DOI 10.1016/j.neucom.2006.10.013, PII S0925231206002876
    • Connally P., Li K., Irwin G. W., Prediction- and simulation-error based perceptron training: solution space analysis and a novel combined training scheme Neurocomputing 2007 70 46 819 827 (Pubitemid 46043979)
    • (2007) Neurocomputing , vol.70 , Issue.4-6 , pp. 819-827
    • Connally, P.1    Li, K.2    Irwin, G.W.3
  • 174
  • 175
    • 0002231381 scopus 로고    scopus 로고
    • Equations of motion from chaotic data: a driven optical fiber ring resonator
    • Voss H. U., Schwache A., Kurths J., Mitschke F., Equations of motion from chaotic data: a driven optical fiber ring resonator Physics Letters A 1999 256 1 47 54
    • (1999) Physics Letters A , vol.256 , Issue.1 , pp. 47-54
    • Voss, H.U.1    Schwache, A.2    Kurths, J.3    Mitschke, F.4
  • 179
    • 33845574392 scopus 로고    scopus 로고
    • Evaluation of dynamical models: dissipative synchronization and other techniques
    • Aguirre L. A., Furtado E. C., Trres L. A. B., Evaluation of dynamical models: dissipative synchronization and other techniques Physical Review E 2006 74 6 16
    • (2006) Physical Review E , vol.74 , Issue.6 , pp. 16
    • Aguirre, L.A.1    Furtado, E.C.2    Trres, L.A.B.3
  • 181
    • 0036010530 scopus 로고    scopus 로고
    • Algorithm for vector autoregressive model parameter estimation using an orthogonalization procedure
    • DOI 10.1114/1.1454134
    • Bagarinao E., Sato S., Algorithm for vector autoregressive model parameter estimation using an orthogonalization procedure Annals of Biomedical Engineering 2002 30 2 260 271 (Pubitemid 34325810)
    • (2002) Annals of Biomedical Engineering , vol.30 , Issue.2 , pp. 260-271
    • Bagarinao, E.1    Sato, S.2
  • 183
    • 21844459472 scopus 로고    scopus 로고
    • Evolution of mathematical models of chaotic systems based on multiobjective genetic programming
    • DOI 10.1007/s10115-004-0184-3
    • Rodrguez-Vzquez K., Fleming P. J., Evolution of mathematical models of chaotic systems based on multiobjective genetic programming Knowledge and Information Systems 2005 8 2 235 256 (Pubitemid 40951992)
    • (2005) Knowledge and Information Systems , vol.8 , Issue.2 , pp. 235-256
    • Rodriguez-Vazquez, K.1    Fleming, P.J.2
  • 184
    • 0000686115 scopus 로고
    • Statistics for mathematical properties of maps between time series embeddings
    • Pecora L. M., Carroll T. L., Heagy J. F., Statistics for mathematical properties of maps between time series embeddings Physical Review E 1995 52 4 3420 3439
    • (1995) Physical Review E , vol.52 , Issue.4 , pp. 3420-3439
    • Pecora, L.M.1    Carroll, T.L.2    Heagy, J.F.3
  • 185
    • 0002492895 scopus 로고
    • Modeling and synchronizing chaotic systems from experimental data
    • Brown R., Rulkov N. F., Tracy E. R., Modeling and synchronizing chaotic systems from experimental data Physics Letters A 1994 194 1-2 71 76
    • (1994) Physics Letters A , vol.194 , Issue.12 , pp. 71-76
    • Brown, R.1    Rulkov, N.F.2    Tracy, E.R.3
  • 187
    • 0035920781 scopus 로고    scopus 로고
    • Identification of coupled map lattice models of complex spatio-temporal patterns
    • Coca D., Billings S. A., Identification of coupled map lattice models of complex spatio-temporal patterns Physics Letters A 2001 287 1-2 65 73
    • (2001) Physics Letters A , vol.287 , Issue.12 , pp. 65-73
    • Coca, D.1    Billings, S.A.2
  • 188
    • 0034801080 scopus 로고    scopus 로고
    • Reconstruction of chaotic dynamics by on-line EM algorithm
    • DOI 10.1016/S0893-6080(01)00094-6, PII S0893608001000946
    • Ishii S., Sato M.-A., Reconstruction of chaotic dynamics by on-line EM algorithm Neural Networks 2001 14 9 1239 1256 (Pubitemid 32910634)
    • (2001) Neural Networks , vol.14 , Issue.9 , pp. 1239-1256
    • Ishii, S.1    Sato, M.-A.2
  • 189
    • 1642333559 scopus 로고    scopus 로고
    • Stability analysis of sleep apnea time series using identified models: a case study
    • Aguirre L. A., Souza. V. P., Stability analysis of sleep apnea time series using identified models: a case study Computers in Biology and Medicine 2004 34 4 241 257
    • (2004) Computers in Biology and Medicine , vol.34 , Issue.4 , pp. 241-257
    • Aguirre, L.A.1    Souza, .V.P.2
  • 190
    • 2342650786 scopus 로고    scopus 로고
    • Scalar modeling and analysis of a 3D biochemical reaction model
    • DOI 10.1016/j.jtbi.2004.02.004, PII S0022519304000530
    • Maquet J., Letellier C., Aguirre L. A., Scalar modeling and analysis of a 3D biochemical reaction model Journal of Theoretical Biology 2004 228 3 421 430 (Pubitemid 38591467)
    • (2004) Journal of Theoretical Biology , vol.228 , Issue.3 , pp. 421-430
    • Maquet, J.1    Letellier, C.2    Aguirre, L.A.3
  • 192
    • 0001595014 scopus 로고
    • Topological characterization and global vector field reconstruction of an experimental electrochemical system
    • Letellier C., Le Sceller L., Dutertre P., Gouesbet G., Fei Z., Hudson J. L., Topological characterization and global vector field reconstruction of an experimental electrochemical system Journal of Physical Chemistry 1995 99 18 7016 7027
    • (1995) Journal of Physical Chemistry , vol.99 , Issue.18 , pp. 7016-7027
    • Letellier, C.1    Le Sceller, L.2    Dutertre, P.3    Gouesbet, G.4    Fei, Z.5    Hudson, J.L.6
  • 193
    • 0000192492 scopus 로고
    • Topological time-series analysis of a string experiment and its synchronized model
    • Tufillaro N. B., Wyckoff P., Brown R., Schreiber T., Molteno T., Topological time-series analysis of a string experiment and its synchronized model Physical Review E 1995 51 1 164 174
    • (1995) Physical Review E , vol.51 , Issue.1 , pp. 164-174
    • Tufillaro, N.B.1    Wyckoff, P.2    Brown, R.3    Schreiber, T.4    Molteno, T.5
  • 194
    • 0030291304 scopus 로고    scopus 로고
    • Topological characterization of reconstructed attractors modding out symmetries
    • Letellier C., Gouesbet G., Topological characterization of reconstructed attractors modding out symmetries Journal de Physique II 1996 6 11 1615 1638 (Pubitemid 126795496)
    • (1996) Journal de Physique II , vol.6 , Issue.11 , pp. 1615-1638
    • Letellier, C.1    Gouesbet, G.2
  • 195
    • 0000576754 scopus 로고    scopus 로고
    • Comparisons of new nonlinear modeling techniques with applications to infant respiration
    • PII S0167278997003114
    • Small M., Judd K., Comparisons of new nonlinear modeling techniques with applications to infant respiration Physica D 1998 117 14 283 298 (Pubitemid 128676604)
    • (1998) Physica D: Nonlinear Phenomena , vol.117 , Issue.1-4 , pp. 283-298
    • Small, M.1    Judd, K.2
  • 196
    • 44049111332 scopus 로고
    • Testing for nonlinearity in time series: the method of surrogate data
    • Theiler J., Eubank S., Longtin A., Galdrikian B., Farmer J. D., Testing for nonlinearity in time series: the method of surrogate data Physica D 1992 58 14 77 94
    • (1992) Physica D , vol.58 , Issue.14 , pp. 77-94
    • Theiler, J.1    Eubank, S.2    Longtin, A.3    Galdrikian, B.4    Farmer, J.D.5
  • 198
    • 0038166236 scopus 로고    scopus 로고
    • Identification of dynamic process systems with surrogate data methods
    • DOI 10.1002/aic.690470917
    • Barnard J. P., Aldrich C., Gerber M., Identification of dynamic process systems with surrogate data methods AIChE Journal 2001 47 9 2064 2075 (Pubitemid 36858805)
    • (2001) AIChE Journal , vol.47 , Issue.9 , pp. 2064-2075
    • Barnard, J.P.1    Aldrich, C.2    Gerber, M.3
  • 199
  • 200
    • 1842842178 scopus 로고    scopus 로고
    • Consistent nonlinear dynamics: identifying model inadequacy
    • McSharry P. E., Smith L. A., Consistent nonlinear dynamics: identifying model inadequacy Physica D 2004 192 1-2 1 22
    • (2004) Physica D , vol.192 , Issue.12 , pp. 1-22
    • Mcsharry, P.E.1    Smith, L.A.2
  • 201
    • 0001581120 scopus 로고
    • Modeling and synchronizing chaotic systems from time-series data
    • Brown R., Rulkov N. F., Tracy E. R., Modeling and synchronizing chaotic systems from time-series data Physical Review E 1994 49 5 3784 3800
    • (1994) Physical Review E , vol.49 , Issue.5 , pp. 3784-3800
    • Brown, R.1    Rulkov, N.F.2    Tracy, E.R.3
  • 206
    • 0027557151 scopus 로고
    • Grey-box modelling and identification using physical knowledge and Bayesian techniques
    • Tulleken H. J. A. F., Grey-box modelling and identification using physical knowledge and Bayesian techniques Automatica 1993 29 2 285 308
    • (1993) Automatica , vol.29 , Issue.2 , pp. 285-308
    • Tulleken, H.J.A.F.1
  • 208
    • 0030109138 scopus 로고    scopus 로고
    • Identification of non-linear systems using empirical data and prior knowledgean optimization approach
    • Johansen T. A., Identification of non-linear systems using empirical data and prior knowledgean optimization approach Automatica 1996 32 3 337 356
    • (1996) Automatica , vol.32 , Issue.3 , pp. 337-356
    • Johansen, T.A.1
  • 209
    • 0036745036 scopus 로고    scopus 로고
    • Using steady-state prior knowledge to constrain parameter estimates in nonlinear system identification
    • Corra M. V., Aguirre L. A., Saldanha R. R., Using steady-state prior knowledge to constrain parameter estimates in nonlinear system identification IEEE Transactions on Circuits and Systems I 2002 49 9 1376 1381
    • (2002) IEEE Transactions on Circuits and Systems I , vol.49 , Issue.9 , pp. 1376-1381
    • Corra, M.V.1    Aguirre, L.A.2    Saldanha, R.R.3
  • 210
    • 2342550660 scopus 로고    scopus 로고
    • Imposing steady-state performance on identified nonlinear polynomial models by means of constrained parameter estimation
    • Aguirre L. A., Barroso M. F. S., Saldanha R. R., Mendes E. M. A. M., Imposing steady-state performance on identified nonlinear polynomial models by means of constrained parameter estimation IEE Proceedings: Control Theory and Applications 2004 151 2 174 179
    • (2004) IEE Proceedings: Control Theory and Applications , vol.151 , Issue.2 , pp. 174-179
    • Aguirre, L.A.1    Barroso, M.F.S.2    Saldanha, R.R.3    Mendes, E.M.A.M.4
  • 211
    • 0039721640 scopus 로고    scopus 로고
    • Models of knowing and the investigation of dynamical systems
    • PII S0167278999000354
    • Rapp P. E., Schmah T. I., Mees A. I., Models of knowing and the investigation of dynamical systems Physica D 1999 132 1-2 133 149 (Pubitemid 129524973)
    • (1999) Physica D: Nonlinear Phenomena , vol.132 , Issue.1-2 , pp. 133-149
    • Rapp, P.E.1    Schmah, T.I.2    Mees, A.I.3
  • 212
    • 41349099820 scopus 로고    scopus 로고
    • Distinguishing between folding and tearing mechanisms in strange attractors
    • Byrne G., Gilmore R., Letellier C., Distinguishing between folding and tearing mechanisms in strange attractors Physical Review E 2004 70 5 9
    • (2004) Physical Review E , vol.70 , Issue.5 , pp. 9
    • Byrne, G.1    Gilmore, R.2    Letellier, C.3
  • 213
    • 33645682375 scopus 로고    scopus 로고
    • Piecewise affine models of chaotic attractors: the Rssler and Lorenz systems
    • Amaral G. F. V., Letellier C., Aguirre L. A., Piecewise affine models of chaotic attractors: the Rssler and Lorenz systems Chaose 2006 16 1 14
    • (2006) Chaose , vol.16 , Issue.1 , pp. 14
    • Amaral, G.F.V.1    Letellier, C.2    Aguirre, L.A.3
  • 214
    • 21344491165 scopus 로고
    • Summary of the second workshop on measures of complexity and chaos
    • Gilmore R., Summary of the second workshop on measures of complexity and chaos International Journal of Bifurcation and Chaos 1993 3 3 491 524
    • (1993) International Journal of Bifurcation and Chaos , vol.3 , Issue.3 , pp. 491-524
    • Gilmore, R.1
  • 215
    • 0000614719 scopus 로고
    • Deterministic models with chaotic dynamics
    • May R. M., Deterministic models with chaotic dynamics Nature 1975 256 5514 165 166
    • (1975) Nature , vol.256 , Issue.5514 , pp. 165-166
    • May, R.M.1
  • 216
    • 0017185443 scopus 로고
    • Simple mathematical models with very complicated dynamics
    • May R. M., Simple mathematical models with very complicated dynamics Nature 1976 261 5560 459 467
    • (1976) Nature , vol.261 , Issue.5560 , pp. 459-467
    • May, R.M.1
  • 217
    • 0002591468 scopus 로고
    • A two-dimensional mapping with a strange attractor
    • Hnon M., A two-dimensional mapping with a strange attractor Communications in Mathematical Physics 1976 50 1 69 77
    • (1976) Communications in Mathematical Physics , vol.50 , Issue.1 , pp. 69-77
    • Hnon, M.1
  • 218
    • 0035143087 scopus 로고    scopus 로고
    • Identifying chaotic systems using wiener and hammerstein cascade models
    • DOI 10.1016/S0895-7177(00)00256-9, PII S0895717700002569
    • Xu M., Chen G., Tian Y.-T., Identifying chaotic systems using Wiener and Hammerstein cascade models Mathematical and Computer Modelling 2001 33 4-5 483 493 (Pubitemid 32122699)
    • (2001) Mathematical and Computer Modelling , vol.33 , Issue.4-5 , pp. 483-493
    • Xu, M.1    Chen, G.2    Tian, Y.-T.3
  • 219
    • 0018508810 scopus 로고
    • MULTIPLE-VALUED STATIONARY STATE AND ITS INSTABILITY OF THE TRANSMITTED LIGHT BY A RING CAVITY SYSTEM.
    • DOI 10.1016/0030-4018(79)90090-7
    • Ikeda K., Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system Optics Communications 1979 30 2 257 261 (Pubitemid 10437376)
    • (1979) Optics Communications , vol.30 , Issue.2 , pp. 257-261
    • Ikeda Kensuke1
  • 220
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • Rssler O. E., An equation for continuous chaos Physics Letters A 1976 57 5 397 398
    • (1976) Physics Letters A , vol.57 , Issue.5 , pp. 397-398
    • Rssler, O.E.1
  • 221
    • 0017714604 scopus 로고
    • Oscillation and chaos in physiological control systems
    • Mackey M. C., Glass L., Oscillation and chaos in physiological control systems Science 1977 197 4300 287 289 (Pubitemid 8130447)
    • (1977) Science , vol.197 , Issue.4300 , pp. 287-289
    • Mackey, M.C.1    Glass, L.2
  • 228
    • 0000331034 scopus 로고    scopus 로고
    • Detecting nonlinearity in multivariate time series
    • Palu M., Detecting nonlinearity in multivariate time series Physics Letters A 1996 213 3-4 138 147
    • (1996) Physics Letters A , vol.213 , Issue.34 , pp. 138-147
    • Palu, M.1
  • 229
    • 0033028702 scopus 로고    scopus 로고
    • Nonlinear multivariable modeling and analysis of sleep apnea time series
    • DOI 10.1016/S0010-4825(99)00006-2, PII S0010482599000062
    • Aguirre L. A., Barros V. C., Souza. V. P., Nonlinear multivariable modeling and analysis of sleep apnea time series Computers in Biology and Medicine 1999 29 3 207 228 (Pubitemid 29284469)
    • (1999) Computers in Biology and Medicine , vol.29 , Issue.3 , pp. 207-228
    • Aguirre, L.A.1    Barros, V.C.2    Souza, A.V.P.3
  • 233
    • 34547340415 scopus 로고    scopus 로고
    • Global models from the Canadian lynx cycles as a direct evidence for chaos in real ecosystems
    • DOI 10.1007/s00285-007-0075-9
    • Maquet J., Letellier C., Aguirre L. A., Global models from the Canadian lynx cycles as a direct evidence for chaos in real ecosystems Journal of Mathematical Biology 2007 55 1 21 39 (Pubitemid 47145808)
    • (2007) Journal of Mathematical Biology , vol.55 , Issue.1 , pp. 21-39
    • Maquet, J.1    Letellier, C.2    Aguirre, L.A.3
  • 237
    • 0035452860 scopus 로고    scopus 로고
    • Learning of Chua's circuit attractors by locally recurrent neural networks
    • DOI 10.1016/S0960-0779(00)00174-0, PII S0960077900001740
    • Cannas B., Cincotti S., Marchesi M., Pilo F., Learning of Chuas circuit attractors by locally recurrent neural networks Chaos, Solitons Fractals 2001 12 11 2109 2115 (Pubitemid 32518186)
    • (2001) Chaos, Solitons and Fractals , vol.12 , Issue.11 , pp. 2109-2115
    • Cannas, B.1    Cincotti, S.2    Marchesi, M.3    Pilo, F.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.