Multi-parameter identification from scalar time series generated by a Malkus-Lorenz water wheel

Chaos

Volumn 22, Issue 1, 2012, Pages

  Illing, Lucas ^a   Saunders, Alison M ^a   Hahs, Daniel ^b  

^a REED COLLEGE   (United States)

^b Torch Technologies Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

WATER;

ALGORITHM; ARTICLE; COMPUTER SIMULATION; ENERGY TRANSFER; METHODOLOGY; MOTION; NONLINEAR SYSTEM; OSCILLOMETRY;

ALGORITHMS; COMPUTER SIMULATION; ENERGY TRANSFER; MOTION; NONLINEAR DYNAMICS; OSCILLOMETRY; WATER;

EID: 84859355247     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3689441     Document Type: Article

References (27)

1. Malkus W.V. R. Mem. Soc. R. Sci. Liege, Collection 6 1972, IV:125.
2. Strogatz S.H. Nonlinear Dynamics and Chaos 1994, (Addison-Wesley, Reading, MA).
3. Illing L. Fordyce R. Saunders A. Ormond B. Experiments with a malkus-lorenz water wheel: Chaos and synchronization. Am. J. Phys. (to be published)
4. Tokuda I. Parlitz U. Illing L. Kennel M. Abarbanel H. AIP Conf. Proc. 2003, 676:251. and.
5. Raue A. Becker V. Klingmuller U. Timmer J. Chaos 2010, 20:045105. 10.1063/1.3528102, and.
6. So P. Ott E. Dayawansa W.P. Phys. Rev. E 1994, 49:2650. 10.1103/PhysRevE.49.2650, and.
7. Abarbanel H.D. I. Creveling D.R. Jeanne J.M. Phys. Rev. E 2008, 77:016208. 10.1103/PhysRevE.77.016208, and.
8. Abarbanel H.D. I. Kostuk M. Whartenby W. Q. J. R. Meteorol. Soc. 2010, 136:769. and.
9. Narendra K.S. Annaswamy A.M. Stable Adaptive Systems 1989, and (Prentice Hall, Englewood Cliffs, New Jersey).
10. Andrievskii B.R. Nikiforov V.O. Fradkov A.L. Autom. Remote Control 2007, 68:1186. 10.1134/S0005117907070077, and.
11. Zhang Q.H. IEEE Trans. Autom. Control 2002, 47:525. 10.1109/9.989154.
12. Yu D.C. Parlitz U. Phys. Rev. E 2008, 77:066221. 10.1103/PhysRevE.77.066221, and.
13. In point of fact, the extended Kalman filter will perform the estimation using the raw measured data (does not need the first derivative), but here the first derivative is employed in keeping with the input to the adaptive filter.
14. Matson L.E. Am. J. Phys. 2007, 75:1114. 10.1119/1.2785209.
15. Sun F. Peng H. Luo Q. Li L. Yang Y. Chaos 2009, 19:023109. 10.1063/1.3127599, and.
16. Boyd S. Sastry S.S. Automatica 1986, 22:629. 10.1016/0005-1098(86)90002-6, and.
17. Ruelle D. Phys. Rev. Lett. 1986, 56:405. 10.1103/PhysRevLett.56.405.
18. Melbourne I. Gottwald G.A. Nonlinearity 2008, 21:179. 10.1088/0951-7715/21/1/010, and.
19. Peng H. Li L. Yang Y. Sun F. Phys. Rev. E 2011, 83:036202. 10.1103/PhysRevE.83.036202, For systems converging to a fixed point, transients can be exploited, as discussed, for example, in and.
20. Krasovskii N.N. Stability of Motion 1963, 58-62. (Stanford University Press, Stanford, CA), pp. (translated by J. L. Brenner).
21. Fradkov A.L. Progromsky A.Y. Introduction to Control of Oscillations and Chaos 1998, p. 51. and (World Scientific, Singapore).
22. Sorrentino F. Ott E. Chaos 2009, 19:033108. 10.1063/1.3186458, and.
23. Mishra A.A. Sanghi S. Chaos 2006, 16:013114. 10.1063/1.2154792, and.
24. Bishop C.H. Etherton B.J. Majumdar S.J. Mon. Weather Rev. 2001, 129:420. 10.1175/1520-0493(2001)129<0420:ASWTET>2.0.CO;2, and.
25. Ott E. Hunt B.R. Szunyogh I. Zimin A.V. Kostelich E.J. Corazza M. Kalnay E. Patil D.J. Yorke J.A. Tellus 2004, 56A:415. and.
26. Annan J.D. Lunt D.J. Hargreaves J.C. Valdes P.J. Nonlinear Processes Geophys. 2005, 12:363. 10.5194/npg-12-363-2005, and.
27. Applied Optimal Estimation 1974, pp. 188. A. Gelb, edited by (MIT, Cambridge, MA).