Inverting chaos: Extracting system parameters from experimental data

Chaos

Volumn 6, Issue 4, 1996, Pages 528-533

  Baker, G L ^a   Gollub, J P ^b,c   Blackburn, J A ^d  

^a Bryn Athyn College of the New Church   (United States)

^b HAVERFORD COLLEGE   (United States)

^c UNIVERSITY OF PENNSYLVANIA   (United States)

^d WILFRID LAURIER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001976684     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166200     Document Type: Article

References (20)

1. See, for example, H. D. I. Abarbanel, Analysis of Observed Chaotic Data (Springer-Verlag, New York, 1995); or H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, "The analysis of observed chaotic data in physical systems," Rev. Mod. Phys. 65, 1331 (1993).
2. See, for example, H. D. I. Abarbanel, Analysis of Observed Chaotic Data (Springer-Verlag, New York, 1995); or H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, "The analysis of observed chaotic data in physical systems," Rev. Mod. Phys. 65, 1331 (1993).
3. R. Brown, N. F. Rulkov, and E. R. Tracy, "Modeling and synchronizing chaotic systems from time-series data," Phys. Rev. E 49, 3784 (1994); R. Brown, N. F. Rulkov, and E. R. Tracy, "Modeling and synchronizing chaotic systems from experimental data," Phys. Lett. A 194, 71 (1994).
4. R. Brown, N. F. Rulkov, and E. R. Tracy, "Modeling and synchronizing chaotic systems from time-series data," Phys. Rev. E 49, 3784 (1994); R. Brown, N. F. Rulkov, and E. R. Tracy, "Modeling and synchronizing chaotic systems from experimental data," Phys. Lett. A 194, 71 (1994).
5. J. L. Breeden and A. Hubler, "Reconstructing equations of motion from experimental data with unobserved variables," Phys. Rev. A 42, 5817 (1992).
6. G. Rowlands and J. C. Sprott, "Extraction of dynamical equations from chaotic data," Physica D 58, 251 (1992).
7. G. Gouesbet, "Reconstruction of vector fields the case of the Lorenz system," Phys. Rev. A 46, 1784 (1992).
8. U. Parlitz, "Estimating model parameters from time series by autosynchronization," Phys. Rev. Lett. 76, 1232 (1996).
9. E. N. Lorenz, "Deterministic non-periodic flow," J. Atmos. Sci. 20, 130 (1963).
10. O. E. Rossler, "An equation for continuous chaos," Phys. Lett. A 57, 397 (1976).
11. See, for example, D. G. Luenberger, Linear and Nonlinear Programming (Addison-Wesley, Reading, MA, 1984).
12. J. A. Blackburn, S. Vik, Wu Binruo, and H. J. T. Smith, "Driven pendulum for studying chaos," Rev. Sci. Instrum. 60, 422 (1989).
13. G. L. Baker and J. P. Gollub, Chaotic Dynamics: An Introduction (Cambridge University Press, Cambridge, 1990, 1996).
14. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge University Press, Cambridge, 1986).
15. P. Grassberger and I. Procaccia, "Characterization of strange attractors," Phys. Rev. Lett. 50, 346 (1983).
16. A. Wolf, J. P. Swift, H. L. Swinney, and J. A. Vastano, "Determining Lyapunov exponents from a time series," Physica D 16, 285 (1985).
17. See, for example, D. P. Lathrop and E. J. Kostelich, "Characterization of an experimental strange attractor by periodic orbits," Phys. Rev. A 40, 4028 (1989).
18. D. P. Vallette, W. S. Edwards, and J. P. Gollub, "Transition to spatiotemporal chaos via spatially subharmonic oscillations of a periodic front," Phys. Rev. E 49, R4783 (1994).
19. F. Daviaud, J. Lega, P. Berge, P. Coullet, and M. DuBois, "Spatiotemporal intermittency in a 1D convective pattern: theoretical model and experiments," Physica D 55, 287 (1992).
20. D. P. Vallette (private communication with J. P. Gollub).