Wavelet reconstruction of nonlinear dynamics

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 8, Issue 11, 1998, Pages 2191-2201

  Allingham, David ^a   West, Matthew ^a   Mees, Alistair I ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032215749     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127498001789     Document Type: Article

References (15)

1. Cao, L., Hong, Y., Fang, H. & He, G. [1995] "Predicting chaotic time series with wavelet networks," Phys. D85, 225-238.
2. Chen, S. S., Donoho, D. L. & Saunders, M. A. [1996] "Atomic decomposition by basis pursuit," unpublished.
3. Daubechies, I. [1992] Ten Lectures on Wavelets, CBMS-NSF Regional Conf. Series in Applied Mathematics, SIAM.
4. Donoho, D. L. [1992] "Unconditional bases are optimal bases for data compression and for statistical estimation," Technical Report, Department of Statistics, Stanford University.
5. Glendinning, P. & Sparrow, C. T. [1983] "Local and global bahaviour near homoclinic orbits," J. Stat. Phys. 35, 645-697.
6. Glendinning, P. & Sparrow, C. T. [1983] "Bifurcations near homoclinic orbits," in XVIth Int. Congress of Theoretical and Applied Mechanics.
7. Judd, K. & Mees, A. I. [1995] "On selecting models for nonlinear time series," Phys. D82, 426-444.
8. Judd, K. & Mees, A. I. [1996] "Modeling chaotic motions of a string from experimental data," Phys. D92, 221-236.
9. Mallat, S. & Zhang, Z. [1993] "Matching pursuit in a time-frequency dictionary," IEEE Trans. Sig. Process. 41, 3397-3415.
10. Marquardt, D. W. [1963] "An algorithm for least-squares estimation of nonlinear parameters," J. SIAM 11, 431-441.
11. Mees, A. I. & Sparrow, C. T. [1987] "Some tools for analyzing chaos," Proc. IEEE 75, 1058-1070.
12. Molteno, T. C. A. & Tufillaro, N. B. [1990] "Torus doubling and chaotic string vibrations: Experimental results," J. Sound Vib. 137, 327-330.
13. Pati, Y. C., Rezaiifar, R. & Krishnaprasad, P. S. [1993] "Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition," in Proc. 27th Asilomar Conf. Signals, Systems and Computers, ed. Singh, A.
14. Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T. [1988] Numerical Recipes in C Cambridge (Cambridge University Press).
15. Rissanen, J. [1989] Stochastic Complexity in Statistical Inquiry, Series in Computer Science 15 (World Scientific, Singapore).