Bivariate surrogate techniques: Necessity, strengths, and caveats

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

Volumn 68, Issue 6 2, 2003, Pages 662021-6620215

  Andrzejak, Ralph G ^a   Kraskov, Alexander ^a   Stögbauer, Harald ^a   Mormann, Florian ^b   Kreuz, Thomas ^a,b  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

^b UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; MATHEMATICAL MODELS; MULTIVARIABLE SYSTEMS; NONLINEAR SYSTEMS; TIME SERIES ANALYSIS;

BIVARIATE SURROGATE TECHNIQUES; DETERMINISTIC MODEL DYNAMICS;

RANDOM PROCESSES;

EID: 1442330397     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (56)

1. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, U.K., 1997).
2. A.R. Osborne and A. Provenzale, Physica D 35, 357 (1989).
3. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J.D. Farmer, Physica D 58, 77 (1992).
4. J. Arnhold, K. Lehnertz, P. Grassberger, and C.E. Elger, Physica D 134, 419 (1999).
5. M. Le Van Quyen, J. Martinerie, C. Adam, and F. Varela, Pysica D 127, 250 (1999).
6. F. Mormann, K. Lehnertz, P. David, and C.E. Elger, Physica D 144, 358 (2000).
7. J. Fell, P. Klaver, K. Lehnertz, T. Grunwald, C. Schaller, C. Elger, and G. Fernández, Nat. Neurosci. 4, 1259 (2001).
8. C.J. Stam and B.W. van Dijk, Physica D 163, 236 (2002).
9. F. Mormann, T. Kreuz, R.G. Andrzejak, P. David, K. Lehnertz, and C.E. Elger, Epilepsy Res. 53, 173 (2003).
10. F. Mormann, R.G. Andrzejak, T. Kreuz, C. Rieke, P. David, C.E. Elger, and K. Lehnertz, Phys. Rev. E 67, 021912 (2003).
11. S.A.R.B. Rombouts, R.W.M. Keunen, and C.J. Stam, Phys. Lett. A 202, 352 (1995).
12. E. Pereda, R. Rial, A. Gamundi, and J. González, Physica D 148, 147 (2001).
13. J. Bhattacharya, H. Petsche, and E. Pereda, J. Neurosci. 21, 6329 (2001).
14. J. Bhattacharya and H. Petsche, Phys. Rev. E 64, 012902 (2001).
15. M. Breakspear and J.R. Terry, Neuroimage 16, 822 (2002).
16. E. Pereda, S. Mañas, L. De Vera, J.M. Garrido, S. López, and J. González, Neurosci. Lett. 337, 101 (2003).
17. J.R. Terry and M. Breakspear, Biol. Cybern. 88, 129 (2003).
18. P.A. Tass, T. Fieseler, J. Dammers, K. Dolan, P. Morosan, M. Majtanik, F. Boers, A. Muren, K. Zilles, and G.R. Fink, Phys. Rev. Lett. 90, 088101 (2003).
19. S.J. Schiff, P. So, T. Chang, R.E. Burke, and T. Sauer, Phys. Rev. E 54, 6708 (1996).
20. R. Quian Quiroga, A. Kraskov, T. Kreuz, and P. Grassberger, Phys. Rev. E 65, 041903 (2002).
21. T.I. Netoff and S.J. Schiff, J. Neurosci. 22, 7297 (2002).
22. F. Censi, V. Barbaro, P. Bartolini, G. Galcagmini, A. Michelucci, and S. Cerutti, Biol. Cybern. 85, 195 (2001).
23. M. Paluš, Phys. Lett. A 213, 138 (1996).
24. M. Paluš, Phys. Lett. A 235, 341 (1997).
25. M. Paluš and D. Hoyer, IEEE Eng. Med. Biol. Mag. 17, 40 (1998).
26. M.G. Rosenblum, L. Cimponeriu, A. Bezerianos, A. Patzak, and R. Mrowka, Phys. Rev. E 65, 041909 (2002).
27. J. Bhattacharya, E. Pereda, and H. Petsche, IEEE Trans. Syst. Man Cybern. B 33, 85 (2003).
28. A. Cenys, G. Lasiene, and K. Pyragas, Physica D 52, 332 (1991).
29. H. Kantz, Phys. Rev. E 49, 5091 (1994).
30. N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, and H.D.I. Abarbanel, Phys. Rev. E 51, 980 (1995).
31. P. Tass, M.G. Rosenblum, J. Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.J. Freund, Phys. Rev. Lett. 81, 3291 (1998).
32. P.J. Franaszczuk and G.K. Bergey, Biol. Cybern, 81, 3 (1999).
33. J.P. Lachaux, E. Rodriguez, J. Martinerie, and F.J. Varela, Hum. Brain Mapp 8, 194 (1999).
34. T. Schreiber, Phys. Rev. Lett. 85, 461 (2000).
35. M.G. Rosenblum and A.S. Pikovsky, Phys. Rev. E 64, 045202(R) (2001).
36. M. Wiesenfeldt, U. Parlitz, and W. Lauterborn, Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, 2217 (2001).
37. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization, A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, U.K., 2001).
38. L. Kocarev and U. Parlitz, Phys. Rev. Lett. 76, 1816 (1996).
39. R. Quian Quiroga, J. Arnhold, and P. Grassberger, Phys. Rev. E 61, 5142 (2000).
40. D. Prichard and J. Theiler, Phys. Rev. Lett. 73, 951 (1994).
41. T. Schreiber, Phys. Rev. Lett. 80, 2105 (1998).
42. T. Schreiber and A. Schmitz, Physica D 142, 346 (2000).
43. K.T. Dolan and A. Neiman, Phys. Rev. E 65, 026108 (2002).
44. F. Takens, in Dynamical Systems and Turbulence, edited by D.A. Rand and L.-S. Young, Lecture Notes in Mathematics, Vol. 898 (Springer-Verlag, Berlin, 1980), pp. 366-381.
45. J. Theiler, Phys. Rev. A 34, 2427 (1986).
46. T. Schreiber and A. Schmitz, Phys. Rev. Lett. 77, 635 (1996).
47. D. Kugiumtzis, Phys. Rev. E 60, 2808 (1999).
48. R.G. Andrzejak, G. Widman, K. Lehnertz, P. David, and C.E. Elger, Epilepsy Res. 44, 129 (2001).
49. R.G. Andrzejak, K. Lehnertz, F. Mormann, C. Rieke, P. David, and C.E. Elger, Phys. Rev. E 64, 061907 (2001).
50. M.G. Rosenblum, A.S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
51. O.E. Rössler, Phys. Lett. A 57, 397 (1976).
52. K.T. Dolan and M.L. Spano, Phys. Rev. E 64, 046128 (2001).
53. D. Kugiumtzis, Phys. Rev. E 62, R25 (2000).
54. J. Timmer, Phys. Rev. E 58, 5153 (1998).
55. R.G. Andrzejak (unpublished).
56. (i) could be used as a surrogate. In that case the power spectrum would be identical to the original, and the amplitude distribution would be practically indistinguishable from that of the original time series (cf. Ref. [47]).