Modeling the basin of attraction as a two-dimensional manifold from experimental data: Applications to balance in humans

Chaos

Volumn 20, Issue 1, 2010, Pages

  Zakynthinaki, Maria S ^a   Stirling, James R ^b   Cordente Martínez, Carlos A ^b   Díaz de Durana, Alfonso López ^b   Quintana, Manuel Sillero ^b   Romo, Gabriel Rodríguez ^b   Molinuevo, Javier Sampedro ^b  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ADULT; ALGORITHM; ARTICLE; BIOPHYSICS; BODY EQUILIBRIUM; HUMAN; MALE; METHODOLOGY; MOVEMENT (PHYSIOLOGY); NONLINEAR SYSTEM; NORMAL DISTRIBUTION; OSCILLOMETRY; STATISTICAL MODEL; STATISTICS; THEORETICAL MODEL;

ADULT; ALGORITHMS; BIOPHYSICS; HUMANS; MALE; MODELS, STATISTICAL; MODELS, THEORETICAL; MOVEMENT; NONLINEAR DYNAMICS; NORMAL DISTRIBUTION; OSCILLOMETRY; POSTURAL BALANCE; STOCHASTIC PROCESSES;

EID: 77953500583     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3337690     Document Type: Article

References (43)

1. Stirling J.R. Zakynthinaki M.S. Chaos 2004, 14:96. CHAOEH, 1054-1500, 10.1063/1.1628451.
2. Stirling J.R. Zakynthinaki M.S. 2005, 64:39. Lecture Notes of the ICB Seminar, Mechanical Loads of the Human Motor System-Injury Prevention(unpublished).
3. Zakynthinaki M.S. Stirling J.R. de Durana A.L. D. Martínez C.A. C. Quintana M.S. Molinuevo J.S. Comput. Phys. Commun. 2008, 179:562. CPHCBZ, 0010-4655, 10.1016/j.cpc.2008.05.003.
4. Milton J.G. Chaos 2009, 19:026101. CHAOEH, 1054-1500, 10.1063/1.3155067.
5. Milton J. Cabrera J.L. Ohira T. Tajima S. Tonosaki Y. Eurich C.W. Campbell S.A. Chaos 2009, 19:026110. CHAOEH, 1054-1500, 10.1063/1.3141429.
6. Ting L.H. van Antwerp K.W. Scrivens J.E. McKay J.L. Welch T.D. J. Bingham J.T. DeWeerth S.P. Chaos 2009, 19:026111. CHAOEH, 1054-1500, 10.1063/1.3142245.
7. Bardy B.G. Oullier O. J. Motor Behav. 2007, 39:326. JMTBAB, 0022-2895, 10.3200/JMBR.39.4.326-336.
8. Bernstein N. The Coordination and Regulation of Movement 1967, (Pergamon, New York, ).
9. Bardy B.G. Oullier O. Bootsma R.J. Stoffregen T.A. J. Exp. Psychol. Hum. Percept. Perform. 2002, 28:499. JPHPDH, 0096-1523, 10.1037/0096-1523.28.3.499.
10. Kay B.A. Hum. Mov. Sci. 1988, 7:343. HMSCDO, 0167-9457, 10.1016/0167-9457(88)90016-4.
11. Nashner L.M. Exp. Brain Res. 1976, 26:59. EXBRAP, 0014-4819, 10.1007/BF00235249.
12. Nashner L.M. McCollum G. Behav. Brain Sci. 1985, 8:135. BBSCDH, 0140-525X, 10.1017/S0140525X00020008.
13. Lauk M. Chow C.C. Pavlik A.E. Collins J.J. Phys. Rev. Lett. 1998, 80:413. PRLTAO, 0031-9007, 10.1103/PhysRevLett.80.413.
14. Hsiao-Wecksler E.T. Katdarea K. Matsona J. Liua W. Lipsitzc L.A. Collins J.J. J. Biomech. 2003, 36:1327. JBMCB5, 0021-9290, 10.1016/S0021-9290(03)00153-2.
15. Riccio G.E. Stoffregen T.A. Hum. Mov. Sci. 1988, 7:265. HMSCDO, 0167-9457, 10.1016/0167-9457(88)90014-0.
16. Yoneda S. Tokumasu K. Acta Oto-Laryngol. 1986, 102:87. AOLAAJ, 0001-6489, 10.3109/00016488609108650.
17. Collins J.J. DeLuca C.J. Phys. Rev. Lett. 1994, 73:764. PRLTAO, 0031-9007, 10.1103/PhysRevLett.73.764.
18. Bardy B.G. Marin L. Stoffregen T.A. Bootsma R.J. J. Exp. Psychol. Hum. Percept. Perform. 1999, 25:1284. JPHPDH, 0096-1523, 10.1037/0096-1523.25.5.1284.
19. McCollum G. Leen T.K. J. Motor Behav. 1989, 21:225. JMTBAB, 0022-2895.
20. Levin A. IEEE Trans. Autom. Control 1994, 39:2471. IETAA9, 0018-9286, 10.1109/9.362845.
21. Cusumano J.R. Kimble B.W. Nonlinear Dyn. 1995, 8:213. NODYES, 0924-090X, 10.1007/BF00045775.
22. Genesio M.T. R. Vicino A. IEEE Trans. Autom. Control 1985, 30:747. IETAA9, 0018-9286, 10.1109/TAC.1985.1104057.
23. Antosiewicz H.A. A Survey of Lyapunov's Second Method 1958, 4:141-166. Contributions to the Theory of Nonlinear Oscillations Princeton University Press, Princeton.
24. Hahn W. Theory and Applications of Lyapunov's Direct Method 1963, (Prentice-Hall, Englewood Cliffs, ).
25. Salle J.P. L. Lefschetz S. Stability by Lyapunov's Direct Method 1961, (Academic, New York, ).
26. Letov A.M. Stability in Nonlinear Control Systems 1961, (Princeton University Press, Princeton, ).
27. Perlmutter D.D. Stability of Chemical Reactors 1972, (Prentice-Hall, Englewood Cliffs, ).
28. Hewit J.R. Storey C. Electron. Lett. 1966, 2:408. ELLEAK, 0013-5194, 10.1049/el:19660342.
29. Paradis W.O. Perlmutter D.D. AIChE J. 1966, 12:13. AICEAC, 0001-1541.
30. Davison E.J. Cowan K.C. Int. J. Control 1969, 9:349. IJCOAZ, 0020-7179, 10.1080/00207176908905756.
31. Texter J. IEEE Trans. Autom. Control 1974, 19:62. IETAA9, 0018-9286, 10.1109/TAC.1974.1100484.
32. Grebogi J.A. Y. C. Ott E. Phys. Rev. Lett. 1986, 56:1011. PRLTAO, 0031-9007, 10.1103/PhysRevLett.56.1011.
33. Lebedev A.I. Sluchinskaya I. Crystallogr. Rep. 2004, 49:594. CYSTE3, 1063-7745.
34. Urai H. IEEE Trans. Magn. 1985, 21:2676. IEMGAQ, 0018-9464, 10.1109/TMAG.1985.1064190.
35. Schwab A.L. Wisse M. 2001, 1-9. Proceedings of DETC'01. ASME 2001 Design Engineering Technical Conferences and Computers and Information in Engineering Conference (unpublished).
36. Pakdaman K. Grotta-Ragazzo C. Malta C.P. Arino O. Vibert J.-F. Neural Networks 1998, 11:509. NNETEB, 0893-6080, 10.1016/S0893-6080(97)00112-3.
37. Stirling J.R. Martínez C.A. C. de Durana A.L. D. Quintana M.S. Analysis of inbalance in elite sport with application to improvement of technique and injury prevention. 2007, Consejo Superior de Deportes Technical Report No. 07/UPB10/07.
38. Zakynthinaki M.S. Stochastic optimization for adaptive correction of atmospheric distortion in astronomical observation. 2001Ph.D. thesis, Technical University of Crete.
39. Zakynthinaki M.S. Saridakis Y.G. Comput. Phys. Commun. 2003, 150:274. CPHCBZ, 0010-4655, 10.1016/S0010-4655(02)00681-1.
40. Zakynthinaki M.S. Stirling J.R. Comput. Phys. Commun. 2007, 176:98. CPHCBZ, 0010-4655, 10.1016/j.cpc.2006.08.005.
41. Stirling J.R. Zakynthinaki M.S. Billat V. Bull. Math. Biol. 2008, 70:1348. BMTBAP, 0092-8240, 10.1007/s11538-008-9302-9.
42. Zakynthinaki M.S. Stirling J.R. Comput. Phys. Commun. 2008, 179:888. CPHCBZ, 0010-4655, 10.1016/j.cpc.2008.07.012.
43. See supplementary material at for Tables 1-6.