Artificial neural network noise reduction method for chaotic attractors

International Journal of Computer Mathematics

Volumn 73, Issue 4, 2000, Pages 417-431

  Smaoui, Nejib ^a  

^a KUWAIT UNIVERSITY   (Kuwait)

Author keywords

[No Author keywords available]

Indexed keywords

CONFORMAL MAPPING; FRACTALS; MATHEMATICAL MODELS; NEURAL NETWORKS; SIGNAL FILTERING AND PREDICTION; SPURIOUS SIGNAL NOISE;

ADDITIVE NOISE; CHAOTIC ATTRACTORS; NOISE REFINEMENT;

CHAOS THEORY;

EID: 0033731429     PISSN: 00207160     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207160008804907     Document Type: Article

References (22)

1. Moss, F., Luginto, L. and Schleich, W. (1990). Noise and Chaos in Nonlinear Dynamical Systems, Cambridge University Press.
2. Vaseghi, S. V. (1996). Advanced Signal Processing and Digital Noise Reduction, John Wiley.
3. Brillinger, D. R. (1980). Data Analysis and Theory, Holden-Day, San Francisco.
4. Kostelich, E. and Yorke, J. A. (1988). Noise reduction in dynamical systems, Phys. Rev. A, 38(3), 1649-1652.
5. Farmer, J. D. and Sidorovich, J. J. (1988). In: Evolution, Learning and Cognition, Ed. Lee, Y. C. Word Scientific, Singapore.
6. Hammel, S. M. (1990). "A noise reduction method for chaotic systems", Phys. Lett., 148(8, 9), 421-428.
7. Anosov, D. V. (1967). "Geodesic flows and closed Riemannian manifolds with negative curvature", Proc. Steklov Inst., Math., p. 90.
8. Bowen, R. (1975). "w-limit sets for Axiom A diffeomorphisms", J. Differential Equations, 18.
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, 8.
10. Casdagli, M. (1989). "Nonlinear prediction of chaotic time series", Physica D 35, 335-356.
11. Hammel, S. M., Yorke, J. A. and Grebogi, C. (1988). "Numerical orbits of chaotic processes represent true orbits", 19(2), 465-469.
12. Hammel, S. M., Yorke, J. A. and Grebogi, C. (1987). "Do numerical orbits of chaotic dynamical processes represent true orbits?", Journal of Complexity, 3, 136-145.
13. Smaoui, N. and Kostelich, E. (1998). "Using chaos to shadow the quadratic map for all time", International Journal of Computer Mathematics, 70, 117-129.
14. Boulard, H. and Wellekens, C. J. (1989). Speech dynamics and recurrent networks. Proc. ICASSP, pp. 33-36.
15. Antsaklis, P. (1990). Neural networks in control systems. IEEE Contr. Syst. Mag., 10(3), 3-5.
16. Pao, J. H. (1989). Adaptive Pattern Recognition and Neural Networks. Addison-Wesley.
17. Lapedes, A. and Farber, R. (1987). Nonlinear signal processing using neural networks: Prediction and signal modelling, preprint, Los Alamos.
18. Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters, J. SIAM, 11, 431-441.
19. Hénon, M. (1976). "A two dimensional mapping with a strange attractor", Comm. Math. Phys, 50, 69-77.
20. 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.
21. Packards, N. et al. (1980). Phys. Rev. Lett., 45(9), 712.
22. Takens, F. (1981). Detecting Strange Attractor in Turbulence, Lecture Notes in Mathematics, Rand, D. and Young, L. (Eds.). Springer Berlin.