Better nonlinear models from noisy data: Attractors with maximum likelihood

Physical Review Letters

Volumn 83, Issue 21, 1999, Pages 4285-4288

  Mc Sharry, Patrick E ^a   Smith, Leonard A ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001086311     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.83.4285     Document Type: Article

References (24)

1. Å. Björck, Numerical Methods for Least Squares Problems (SIAM, Philadelphia, 1996).
2. P. Grassberger, T. Schreiber, and C. Schaffrath, Int. J. Bifurcation Chaos Appl. Sci. Eng., 1, 521 (1991).
3. L. Jaeger and H. Kantz, Chaos, 6, 440 (1996)
4. H. Kantz and L. Jaeger, Physica (Amsterdam), 109D, 59 (1997).
5. S. Van Huffel and J. Vandewalle, The Total Least Squares Problem (SIAM, Philadelphia, 1991).
6. E. J. Kostelich, Physica (Amsterdam), 58D, 138 (1992).
7. R. M. May, Nature (London), 261, 459 (1976).
8. G. Casella and R. L. Berger, Statistical Inference (Wadsworth and Brooks/Cole, California, 1990).
9. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, 1992), 2nd ed.
10. T. Schreiber, Chaos, 5, 349 (1995).
11. R. M. May and G. Oyster, Am. Nat., 110, 573 (1976)
12. P. A. P. Moran, Biometrics, 6, 250 (1950)
13. W. E. Ricker, J. Fish. Res. Bd. Can., 11, 559 (1954).
14. M. Hénon, Commun. Math. Phys., 50, 69 (1976).
15. L. A. Smith, in Nonlinearity in Geophysics and Astrophysics, Proceedings of the International School of Physics “Enrico Fermi”, Course CXXXIII, G. Cini (Il Nuovo Cimento, Bologna, 1997), pp. 177–246
16. I. Gilmour and L. A. Smith, in Applied Nonlinear Dynamics and Stochastic Systems near the Millennium, J. B. Kadtke and A. Bulsara (AIP, New York, 1997), pp. 335–340.
17. I. Gilmour, Ph.D. thesis, University of Oxford, 1998
18. E. Baake, M. Baake, H. Bock, and K. Briggs, Phys. Rev. A, 45, 5524 (1992)
19. J. Timmer, Int. J. Bifurcation Chaos Appl. Sci. Eng., 8, 1505 (1998)
20. W. Jansen and U. Kriegel, in Lotka-Volterra-Approach to Cooperation and Competition in Dynamic Systems, W. Ebeling and M. Peschel (Akademie-Verlag, Berlin, 1985), pp. 114–122.
21. M. L. Berliner, J. Am. Stat. Assoc., 86, 938 (1991).
22. M. Casdagli, S. Eubank, J. D. Farmer, and J. Gibson, Physica (Amsterdam), 51D, 52 (1991)
23. L. A. Smith, Physica (Amsterdam), 58D, 50 (1992)
24. L. A. Smith, Philos. Trans. R. Soc. London A, 348, 371 (1994).