On identifying global nonlinear discrete models from chaotic data

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 7, Issue 11, 1997, Pages 2593-2601

  Mendes, Eduardo M A M ^a   Billings, S A ^b  

^a Fundacao de Ensino Sup de Sao J   (Brazil)

^b UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031278997     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127497001758     Document Type: Article

References (26)

1. Aguirre, L. A. & Billings, S. A. [1994] "Discrete reconstruction of strange attractors in Chua's circuit," Int. J. Bifurcation and Chaos 4(4), 853-864.
2. Aguirre, L. A. & Billings, S. A. [1995] "Improved structure selection for nonlinear models based on term clustering," Int. J. Control 62, 569-587.
3. Aguirre, L. A. & Mendes, E. M. A. M. [1996] "Global nonlinear polynomial models: Structure, Term cluster and Fixed points," Int. J. Bifurcation and Chaos 6(2), 279-294.
4. Billings, S. A. & Jones, G. N. [1988] "Orthogonal least squares parameter estimation algorithms for nonlinear stochastic systems," Int. J. Syst. Sci. 23(7), 123-142.
5. Billings, S. A. & Jones, G. N. [1992] "Improved techniques for identification of nonlinear stochastic systems," Int. J. Control 50(5), 1873-1896.
6. Billings, S. A., Korenberg, M. & Chen, S. [1988], "Identification of nonlinear output-affine systems using an orthogonal least-squares algorithm," Int. J. Syst. Sci. 19(8), 1559-1568.
7. Billings, S. A., Chen, S. & Korenberg, M. J. (1989), "Identification of MIMO non-linear systems using a forward-regression orthogonal estimator," Int. J. Control 49(6), 2157-2189.
8. Chen, S. & Billings, S. A. [1989] "Representations of non-linear systems: The NARMAX model," Int. J. Control 49(3), 1013-1032.
9. Chen, S., Billings, S. A. & Luo, W. [1989] "Orthogonal least squares methods and their application to non-linear system identification," Int. J. Control 50(5), 1873-1896.
10. Chua, L. O. & Hasler, M. [1993] (Guest Eds.) Special issue on Chaos in Nonlinear Electronic Circuits, IEEE Trans. Circuits Syst. 40(10,11).
11. Eckmann, J. P., Kamphorst, S. O., Ruelle, D. & Ciliberto, S. [1986] "Liapunov exponents from time series," Phys. Rev. A34(6), 4971-4979.
12. Elgar, S. & Chandran, V. [1993] "Higher-order spectral analysis to detect nonlinear interactions in measured time series and an application to Chua's circuit," Int. J. Bifurcation and Chaos 3(1), 19-34.
13. Elgar, S. & Kennedy, M. P. [1993] "Bispectral analysis of Chua's circuit," J. Circuits Syst. Comp. 3(1), 33-48.
14. Glover, J. & Mees, A. I. [1993] "Reconstructing the dynamics of Chua's circuit," J. Circuits Syst. Comp. 3(1), 201-214.
15. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields (Springer-Verlag, New York).
16. Haber, H. & Unbehauen, H. [1990] "Structure identification of nonlinear dynamic systems - A survey on input/output approaches," Automatica 26(4), 651-677.
17. Khibnik, A. I., Roose, D. & Chua, L. O. [1993] "On periodic orbits and homoclinic bifurcations in Chua's circuit with a smooth nonlinearity," Int. J. Bifurcation and Chaos 3(2), 363-384.
18. Korenberg, M., Billings, S. A., Liu, Y. P. & McIlroy, P. J. [1988] "Orthogonal parameter estimation algorithm for non-linear stochastic systems," Int. J. Control 48(1), 193-210.
19. Kortmann, M. & Unbehauen, H. [1988a] "Two algorithms for model structure determination of nonlinear dynamic systems with applications to industrial process," in 8th IFAC Symp. Identification and System Parameter Estimation, Peking, China, pp. 939-946.
20. Kortmann, M. & Unbehauen, H. [1988b] "A model structure selection algorithm in the identification of multi-variable systems with application to a turbogenerator set," in 12th IMACS World Congress on Scientific Computation, Paris, 18-22 July, 1988.
21. Leontaritis, I. J. & Billings, S. A. [1985a] "Input-output parametric models for nonlinear systems - Part I: Deterministic non-linear systems," Int. J. Control 41(2), 303-328.
22. Leontaritis, I. J. & Billings, S. A. [1985b] "Input-output parametric models for non-linear systems - Part I: Stochastic nonlinear systems," Int. J. Control 41(2), 329-344.
23. Madan, R. A. [1993] Special issue on Chua's Circuit: A Paradigm for Chaos, J. Circuits Syst. Comp. 3(1).
24. Mendes, E. M. A. M. & Billings, S. A. [1996] "On over-parametrization of global nonlinear discrete models," Int. J Bifurcation and Chaos, (accepted).
25. Parlitz, U. [1993] "Lyapunov exponents from Chua's circuit," J. Circuits Syst. Comp. 3(2), 507-523.
26. Pottmann, M., Unbehauen, H. & Seborg, D. E. [1993] "Application of a general multi-model approach for identification of highly nonlinear system - A case study," Int. J. Control 57(1), 197-120.