Observability of nonlinear dynamics: Normalized results and a time-series approach

Chaos

Volumn 18, Issue 1, 2008, Pages

  Aguirre, Luis A ^a   Bastos, Saulo B ^a   Alves, Marcela A ^a   Letellier, Christophe ^b  

^a FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

^b Unité Mixte de Recherche   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 41549106640     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2885386     Document Type: Article

References (34)

1. J. Maquet, C. Letellier, and L. A. Aguirre, J. Theor. Biol. 228, 421 (2004).
2. J. Madár, J. Abonyi, and F. Szeifert, Ind. Eng. Chem. Res. 44, 3178 (2005).
3. A. Sitz, U. Schwarz, and J. Kurths, Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, 2093 (2004).
4. L. A. B. Tôrres, Physica D 228, 31 (2007).
5. T. Kailath, Linear Systems (Prentice Hall, Englewood Cliffs, NJ, 1980).
6. L. A. Aguirre, IEEE Trans. Educ. 38, 33 (1995).
7. H. J. Sussman and V. J. Jundjeric, J. Differ. Equations 12, 95 (1972).
8. A. J. Krener, SIAM J. Control 12, 43 (1974).
9. C. Letellier and L. A. Aguirre, Chaos 12, 549 (2002).
10. C. Letellier, J. Maquet, L. Le Sceller, G. Gouesbet, and L. A. Aguirre, J. Phys. A 31, 7913 (1998).
11. C. Letellier, L. A. Aguirre, and J. Maquet, Phys. Rev. E 71, 056202 (2005).
12. L. M. Hively, V. A. Protopopescu, and P. C. Gailey, Chaos 10, 864 (2000).
13. L. A. Aguirre and C. Letellier, J. Phys. A 38, 6311 (2005).
14. L. F. Zhang, Q. M. Zhu, and A. Longden, Int. J. Syst. Sci. 38, 47 (2007).
15. Q. M. Zhu, L. F. Zhang, and A. Longden, Automatica 43, 1519 (2007).
16. M. Casdagli, S. Eubank, J. D. Farmer, and J. Gibson, Physica D 51, 52 (1991).
17. G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. (Johns Hopkins, London, 1989).
18. O. E. Rössler, Phys. Lett. 57A, 397 (1976).
19. T. Buzug and G. Pfister, Physica D 58, 127 (1992).
20. L. M. Pecora, L. Moniz, J. Nichols, and T. L. Carroll, Chaos 17, 013110 (2007).
21. M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992).
22. L. Cao, Physica D 110, 43 (1997).
23. A. M. Fraser and H. L. Swinney, Phys. Rev. A 33, 1134 (1986).
24. A. M. Albano, A. Passamante, and M. E. Farrell, Physica D 54, 85 (1991).
25. G. Kember and A. C. Fowler, Phys. Lett. A 179, 72 (1993).
26. L. A. Aguirre, Phys. Lett. A 203, 88 (1995).
27. O. E. Rössler, Phys. Lett. 71A, 155 (1979).
28. M. H́non and C. Heiles, Astron. J. 69, 73 (1964).
29. T. Matsumoto, L. O. Chua, and K. Tokumasu, IEEE Trans. Circuits Syst. 33, 828 (1986).
30. E. Lorenz, J. Atmos. Sci. 20, 130 (1963).
31. C. Letellier and L. A. Aguirre, Phys. Rev. E 72, 056202 (2005).
32. L. A. Aguirre, G. G. Rodrigues, and E. M. Mendes, Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, 1411 (1997).
33. C. Letellier, G. Gouesbet, and N. Rulkov, Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, 2531 (1996).
34. R. Miranda and E. Stone, Phys. Lett. A 178, 105 (1993).