Modeling chaotic motions of a string from experimental data

Physica D: Nonlinear Phenomena

Volumn 92, Issue 3-4, 1996, Pages 221-236

  Judd, Kevin ^a   Mees, Alistair ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000219046     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(95)00287-1     Document Type: Article

References (21)

1. H.D.I. Abarbanel, R. Brown, J.J. Sidorowich and L.S. Tsimring, Analysis of Observed Chaotic Data, Vol. 65(4), 1993.
2. H.D.I. Abarbanel and M.B. Kennel, Local false nearest neighbors and dynamical dimensions from observed chaotic data, Technical report, Department of Physics, University of California, San Diego (1992).
3. H. Akaike, A new look at the statistical identification model, IEEE Trans. Ann. Control 19 (1974) 716-723.
4. A.K. Bajaj and J.M. Johnson, On the amplitude dynamics and crisis in resonant motion of stretched strings, Phil. Trans. R. Soc. Lond. A 338 (1992) 1-41.
5. R. Brown, Orthonormal polynomials as prediction functions in arbitrary phase space dimensions, Technical report, Institute for Nonlinear Science, University of California at San Diego (1992).
6. J.D. Farmer and J.J. Sidorowich, Optimal shadowing and noise reduction, Physica D 47 (1991) 373-392.
7. P. Glendinning and C. Sparrow, Bifurcations near homoclinic orbits, in XVIth International Congress of Theoretical and Applied Mechanics (1984).
8. P. Glendinning and C.T. Sparrow, Local and global behavior near homoclinic orbits, J. Stat. Phys. 35 (1983) 645-697.
9. K. Judd and A.I. Mees, A model selection algorithm for nonlinear time series, Physica D 82 (1995) 426-444.
10. K. Judd and A.I. Mees, Modeling chaotic motions of a string from experimental data, submitted for publication (1995).
11. K. Judd and A.I. Mees, A simulated annealing approach model selection for highly nonlinear systems, in preparation (1995).
12. K. Judd, A.I. Mees, K. Aihara and M. Toyoda, Grid imaging for a two-dimensional map, Intern. J. Bifurc. & Chaos 1(1) (1991) 197-210.
13. A.I. Mees, Parsimonious dynamical reconstruction, International Journal of Bifurcation and Chaos 3 (1993) 669-675.
14. A.I. Mees and C.T. Sparrow, Some tools for analyzing chaos, Proceedings IEEE 75 (1987) 1058-1070.
15. T. Molteno and N.B. Tufillaro, J. Sound Vib. 137 (1990) 327.
16. J. Rissanen, Stochastic Complexity in Statistical Inquiry, Vol. 15 (World Scientific, Singapore, 1989).
17. T. Sauer, J.A. Yorke and M. Casdagli, Embedology, J. Stat. Phys. 65 (1992) 579-616.
18. G. Schwarz, Estimating the dimension of a model, Ann. Stat. 6 (2) (1977) 461-464.
19. L.P. Shil'nikov, A case of the existence of a denumerable set of periodic motions, Sov. Math. Dokl. 6 (1965) 163-166.
20. L.P. Shil'nikov, On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle-type, Math. USSR Sb. 6 (1968) 427-438.
21. F. Takens, Detecting strange attractors in turbulence, in D.A. Rand and L.S. Young, editors, Dynamical Systems and Turbulence, Vol. 898 (Springer, Berlin, 1981) pp. 365-381.