Reconstructed dynamics and chaotic signal modeling

A nonlinear AR model is derived from the reconstructed dynamics of a signal. The underlying system is assumed to be nonlinear, autonomous, and deterministic. In this formulation, the output error scheme is shown to be more suitable than the equation error scheme in training a network as a nonlinear AR model of the signal. A method to incorporate the information of the dynamical invariants in signal modeling is proposed.<<ETX>>

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

[2]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[3]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[4]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[5]  Sawada,et al.  Measurement of the Lyapunov spectrum from a chaotic time series. , 1985, Physical review letters.

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

[7]  L. Chua,et al.  Chaos: A tutorial for engineers , 1987, Proceedings of the IEEE.

[8]  秦 浩起,et al.  Characterization of Strange Attractor (カオスとその周辺(基研長期研究会報告)) , 1987 .

[9]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

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

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

[12]  A. Lapedes,et al.  Nonlinear signal processing using neural networks: Prediction and system modelling , 1987 .

[13]  J. Shynk.  Adaptive IIR filtering , 1989, IEEE ASSP Magazine.

[14]  David E. Rumelhart,et al.  Predicting the Future: a Connectionist Approach , 1990, Int. J. Neural Syst..

[15]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[16]  Michael C. Mozer,et al.  A Focused Backpropagation Algorithm for Temporal Pattern Recognition , 1989, Complex Syst..

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