Dynamical effects of overparametrization in nonlinear models

[1]  H. Akaike.  A new look at the statistical model identification , 1974 .

[2]  R. Kashyap.  A Bayesian comparison of different classes of dynamic models using empirical data , 1977 .

[3]  B. G. Quinn,et al.  The determination of the order of an autoregression , 1979 .

[4]  Stephen A. Billings,et al.  Identi cation of nonlinear systems-A survey , 1980 .

[5]  Yoshisuke Ueda,et al.  Steady Motions Exhibited by Duffing's Equation : A Picture Book of Regular and Chaotic Motions (Functional Differential Equations) , 1980 .

[6]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[7]  Norio Akamatsu,et al.  Chaotically transitional phenomena in the forced negative-resistance oscillator , 1980 .

[8]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[9]  P. Holmes,et al.  New Approaches to Nonlinear Problems in Dynamics , 1981 .

[10]  I. J. Leontaritis,et al.  Input-output parametric models for non-linear systems Part II: stochastic non-linear systems , 1985 .

[11]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[12]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[13]  S. A. Billings,et al.  Experimental design and identifiability for non-linear systems , 1987 .

[14]  James P. Crutchfield,et al.  Equations of Motion from a Data Series , 1987, Complex Syst..

[15]  G. P. King,et al.  Topological dimension and local coordinates from time series data , 1987 .

[16]  E. Dowell,et al.  Chaotic Vibrations: An Introduction for Applied Scientists and Engineers , 1988 .

[17]  J. Cremers,et al.  Construction of Differential Equations from Experimental Data , 1987 .

[18]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[19]  Martin Casdagli,et al.  Nonlinear prediction of chaotic time series , 1989 .

[20]  Sheng Chen,et al.  Identification of MIMO non-linear systems using a forward-regression orthogonal estimator , 1989 .

[21]  I. G. Kevrekidis,et al.  Application of neural nets to system identification and bifurcation analysis of real world experimental data , 1990 .

[22]  N. F. Jr. Hunter,et al.  Application of nonlinear time series models to driven systems , 1990 .

[23]  H. Abarbanel,et al.  Prediction in chaotic nonlinear systems: Methods for time series with broadband Fourier spectra. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[24]  Zoran Aleksic,et al.  Estimating the embedding dimension , 1991 .

[25]  H. Abarbanel,et al.  Noise reduction in chaotic time series using scaled probabilistic methods , 1991 .

[26]  P. Linsay.  An efficient method of forecasting chaotic time series using linear interpolation , 1991 .

[27]  P. Grassberger,et al.  NONLINEAR TIME SEQUENCE ANALYSIS , 1991 .

[28]  G. W. Bruyn.  Neural networks: Biological computers or electronic brains By R. Moreau et al. (eds.) Les Entretiens de Lyon, proceedings intern. conf. 1990, Springer-Verlag, ISBN 3-54059540-6 195 pages, DM 79.00, Berlin, Heidelberg, New York , 1991, Journal of the Neurological Sciences.

[29]  Jose C. Principe,et al.  Prediction of Chaotic Time Series with Neural Networks , 1992 .

[30]  S. A. Billings,et al.  Neural networks and system identification , 1992 .

[31]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[32]  Martin Casdagli,et al.  Nonlinear Modeling And Forecasting , 1992 .

[33]  L. Chua.  The Genesis of Chua's circuit , 1992 .

[34]  Kennel,et al.  Method to distinguish possible chaos from colored noise and to determine embedding parameters. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[35]  James B. Kadtke,et al.  GLOBAL DYNAMICAL EQUATIONS AND LYAPUNOV EXPONENTS FROM NOISY CHAOTIC TIME SERIES , 1993 .

[36]  Alistair Mees.  PARSIMONIOUS DYNAMICAL RECONSTRUCTION , 1993 .

[37]  S. Masri,et al.  Identification of Nonlinear Dynamic Systems Using Neural Networks , 1993 .

[38]  L. A. Aguirre,et al.  Validating Identified Nonlinear Models with Chaotic Dynamics , 1994 .

[39]  S. A. Billings,et al.  DISCRETE RECONSTRUCTION OF STRANGE ATTRACTORS OF CHUA’S CIRCUIT , 1994 .

[40]  Jan Awrejcewicz,et al.  Bifurcation and Chaos , 1995 .

[41]  Eduardo M. A. M. Mendes,et al.  Smoothing data with Local Instabilities for the Identification of Chaotic Systems. , 1996 .