Modeling continuous processes from data

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 65, Issue 4, 2002, Pages

  Small, Michael ^a,b   Judd, Kevin ^b   Mees, Alistair ^b  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DATA REDUCTION; ERROR ANALYSIS; INTEGRATION; MATHEMATICAL MODELS; POLYNOMIALS; VECTORS;

ADAMS INTEGRATION; FINITE DISCRETE TIME SERIES; LORENTZ SYSTEMS; RADIAL BASIS MAP MODELS;

TIME SERIES ANALYSIS;

EID: 41349090552     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.046704     Document Type: Article

References (39)

1. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis, Cambridge Nonlinear Science Series Vol. 7 (Cambridge University Press, Cambridge, UK, 1997).
2. K. Judd and A. Mees, Physica D 82, 426 (1995).
3. M. J. D. Powell, in Advances in Numerical Analysis, Wavelets, Subdivision Algorithms and Radial Basis Functions, Vol. II edited by W. Light, (Oxford Science Publications, Oxford 1992), Chap. 3, pp. 105-210.
4. G. Gouesbet, Phys. Rev. A 43, 5321 (1991).
5. G. Gouesbet and J. Maquet, Physica D 58, 202 (1992).
6. G. Rowlands and J. Sprott, Physica D 58, 251 (1992).
7. G. Gouesbet and C. Letellier, Phys. Rev. E 49, 4955 (1994).
8. C. Letellier, L.L. Sceller, E. Maréchal, P. Dutertre, B. Maheu, G. Gouesbet, Z. Fei, and J. Hudson, Phys. Rev. E 51, 4262 (1995).
9. A.I. Mees, Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, 777 (1991).
10. A. Irving and T. Dewson, Physica D 102, 15 (1997).
11. X. Zhao and V.Z. Marmarelis, Automatica 33, 81 (1997).
12. R. Brown, N.F. Rulkov, and E.R. Tracy, Phys. Lett A 194, 71 (1994).
13. R. Brown, N.F. Rulkov, and E.R. Tracy, Phys. Rev. E 49, 3784 (1994).
14. L. Fox and F. Mayers, Computing Methods For Scientists and Engineers, Monographs on numerical analysis (Clarendon Press, Oxford, 1968).
15. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, UK, 1988).
16. N.B. Tufillaro, P. Wyckoff, R. Brown, T. Schreiber, and T. Molteno, Phys. Rev. E 51, 164 (1995).
17. J. Rissanen, Stochastic Complexity in Statistical Inquiry (World Scientific, Singapore, 1989).
18. M. Giona, F. Lentini, and V. Cimagalli, Phys. Rev. A 44, 3496 (1991).
19. N. Rul'kovl and A. Volkovskii, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 669 (1992).
20. H. Akaike, IEEE Trans. Autom. Control 19, 716 (1974).
21. G. Schwarz, Ann. Stat. 6, 461 (1978).
22. F. Takens, Lect. Notes Math. 898, 366 (1981).
23. K. Judd and M. Small, Physica D 136, 31 (2000).
24. L. Aguirre and S.A. Billings, Physica D 80, 26 (1995).
25. S. Chen, S.A. Billings, C.F.N. Cowan, and P.M. Grant, Int. J. Control 52, 1327 (1990).
26. E. Cheney, Introduction to Approximation Theory, 2nd ed. (American Mathematical Society, Providence, RI, 1982).
27. M. Small and K. Judd, Physica D 117, 283 (1998).
28. H.D. Abarbanel, Z. Gills, C. Liu, and R. Roy, Phys. Rev. A 53, 440 (1996).
29. K. Judd and A. Mees, Physica D 92, 221 (1996).
30. T. Ikeguchiand K. Aihara, J. Intell. Fuzzy Syst. 5, 33 (1997).
31. M. Small and K. Judd, Physica D 120, 386 (1998).
32. O. Ménard, C. Letellier, J. Maquet, and G. Gouesbet, Phys. Rev. E 62, 6325 (2000).
33. J.P. Crutchfield and B.S. McNamara, Complex Syst. 1, 417 (1987).
34. L. Aguirre and S.A. Billings, Int. J. Control 62, 569 (1995).
35. B.P. Bezruchko, T.V. Dikanev, and D.A. Smirnov, Phys. Rev. E 64, 036210 (2001).
36. C. Letellier, E. Ringuet, J. Maquet, B. Maheu, and G. Gouesbet, Entropie 202/203, 147 (1997).
37. M. Small and K. Judd, Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 1231 (1998).
38. n) will not be correlated. Hence, the free run predictions will rapidly diverge from the expected system dynamics.
39. MATLAB's ODE23, ODE45, ODE113, ODE15S, and ODE23S functions.