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Original Articles

An artificial neural network noise reduction method for chaotic attractors

Pages 417-431 | Received 15 Jan 1999, Published online: 19 Mar 2007

References

  • Moss , F , Luginto , L and Schleich , W . 1990 . Noise and Chaos in Nonlinear Dynamical Systems , Cambridge University Press .
  • Vaseghi , S.V . 1996 . Advanced Signal Processing and Digital Noise Reduction , John Wiley .
  • Brillinger , D.R . 1980 . Data Analysis and Theory , San Francisco : Holden-Day .
  • Kostelich , E and Yorke , J.A . 1988 . Noise reduction in dynamical systems . Phys. Rev. A , 38 ( 3 ) : 1649 – 1652 .
  • Farmer , J.D and Sidorovich , J.J . 1988 . Evolution, Learning and Cognition , Edited by: Lee , Y.C . Singapore : Word Scientific .
  • Hammel , S.M . 1990 . A noise reduction method for chaotic systems . Phys. Lett , 148 ( 8,9 ) : 421 – 428 .
  • Anosov , D.V . 1967 . Geodesic flows and closed Riemannian manifolds with negative curvature . Proc. Steklov Inst.t Math , 148 ( 8,9 ) : 90
  • Bowen , R . 1975 . w-limit sets for Axiom A diffeomorphisms . J. Differential Equations , 18 ( 8,9 )
  • Smaoui , N and AL-Adwani , S . 1997 . Using artificial neural networks to model chaotic time series of ethernet traffic . Journal of Mathematical Modelling and Scientific Computing , 18 ( 8 )
  • Casdagli , M . 1989 . Nonlinear prediction of chaotic time series . Physica D , 35 ( 8 ) : 335 – 356 .
  • Hammel , S.M , Yorke , J.A and Grebogi , C . 1988 . Numerical orbits of chaotic processes represent true orbits , 19 ( 2 ) : 465 – 469 .
  • Hammel , S.M , Yorke , J.A and Grebogi , C . 1987 . Do numerical orbits of chaotic dynamical processes represent true orbits? . Journal of Complexity , 3 ( 2 ) : 136 – 145 .
  • Smaoui , N and Kostehch , E . 1998 . Using chaos to shadow the quadratic map for all time . International Journal of Computer Mathematics , 70 ( 2 ) : 117 – 129 .
  • Boulard , H and Wellekens , C.J . 1989 . Speech dynamics and recurrent networks . Proc. ICASSP , 70 ( 2 ) : 33 – 36 .
  • Antsaklis , P . 1990 . Neural networks in control systems . IEEE Contr. Syst. Mag , 10 ( 3 ) : 3 – 5 .
  • Pao , J.H . 1989 . Adaptive Pattern Recognition and Neural Networks , Addison-Wesley .
  • Lapedes , A and Farber , R . 1987 . Nonlinear signal processing using neural networks:Prediction and signal modelling Los Alamos preprint
  • Marquardt , D.W . 1963 . An algorithm for least-squares estimation of nonlinear parameters . J. SIAM , 11 : 431 – 441 .
  • Hénon , M . 1976 . A two dimensional mapping with a strange attractor . Comm. Math. Phys , 50 : 69 – 77 .
  • Billings , S.A , Jamaluddin , H.B and Chen , S . 1992 . Properties of neural networks with applications to modelling nonlinear dynamical system . Int. J. Control , 55 : 193 – 224 .
  • Packards , N . 1980 . Phys. Rev. Lett , 45 ( 9 ) : 712
  • Takens , F . 1981 . Detecting Strange Attractor in Turbulence, Lecture Notes in Mathematics , Edited by: Rand , D . Springer Berlin .

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