Approach to predictability via anticipated synchronization.

Predictability of chaotic systems is limited, in addition to the precision of the knowledge of the initial conditions, by the error of the models used to extract the nonlinear dynamics from the time series. In this paper, we analyze the predictions obtained from the anticipated synchronization scheme using a chain of slave neural network approximate replicas of the master system. We compare the maximum prediction horizons obtained with those attainable using standard prediction techniques.

[1]  E. Lorenz Deterministic nonperiodic flow , 1963 .

[2]  O. Rössler An equation for continuous chaos , 1976 .

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

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

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

[6]  Murray Z. Frank,et al.  CHAOTIC DYNAMICS IN ECONOMIC TIME‐SERIES , 1988 .

[7]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

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

[9]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[10]  Brown,et al.  Modeling and synchronizing chaotic systems from time-series data. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  J. Suykens,et al.  Learning a simple recurrent neural state space model to behave like Chua's double scroll , 1995 .

[12]  Hal S. Stern,et al.  Neural networks in applied statistics , 1996 .

[13]  Garrison W. Greenwood,et al.  Training multiple-layer perceptrons to recognize attractors , 1997, IEEE Trans. Evol. Comput..

[14]  Enrique Castillo,et al.  Nonlinear time series modeling and prediction using functional networks. Extracting information masked by chaos , 1998 .

[15]  José Manuel Gutiérrez,et al.  Synchronizing chaotic systems with positive conditional Lyapunov exponents by using convex combinations of the drive and response systems , 1998 .

[16]  Kestutis Pyragas SYNCHRONIZATION OF COUPLED TIME-DELAY SYSTEMS : ANALYTICAL ESTIMATIONS , 1998 .

[17]  Voss,et al.  Anticipating chaotic synchronization , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Henning U. Voss,et al.  A backward time shift filter for nonlinear delayed-feedback systems , 2001 .

[19]  H U Voss,et al.  Dynamic long-term anticipation of chaotic states. , 2001, Physical review letters.

[20]  C. Masoller Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback. , 2001, Physical review letters.

[21]  Henning U. Voss,et al.  Real-Time Anticipation of Chaotic States of an Electronic Circuit , 2002, Int. J. Bifurc. Chaos.

[22]  Yoshiro Takiguchi,et al.  Experimental observation of complete chaos synchronization in semiconductor lasers , 2002 .

[23]  Emilio Hernández-García,et al.  Anticipating the dynamics of chaotic maps , 2001, nlin/0111011.

[24]  H U Voss,et al.  Synchronization of reconstructed dynamical systems. , 2003, Chaos.

[25]  Claudio R Mirasso,et al.  Anticipating the response of excitable systems driven by random forcing. , 2002, Physical review letters.

[26]  O. Calvo,et al.  Characterization of the anticipated synchronization regime in the coupled FitzHugh–Nagumo model for neurons , 2003 .

[27]  R. Toral,et al.  Dynamical mechanism of anticipating synchronization in excitable systems. , 2004, Physical review letters.

[28]  S Boccaletti,et al.  Convective instabilities of synchronization manifolds in spatially extended systems. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Raúl Toral,et al.  COUPLING AND FEEDBACK EFFECTS IN EXCITABLE SYSTEMS: ANTICIPATED SYNCHRONIZATION , 2004 .