Decaying of phase synchronization in parkinsonian tremor

Physica A: Statistical Mechanics and its Applications

Volumn 366, Issue , 2006, Pages 552-560

  Gozolchiani, Avi ^a   Moshel, Shay ^a   Hausdorff, Jeffrey M ^b   Simon, Ely ^b   Kurths, Jürgen ^c   Havlin, Shlomo ^a  

^a BAR ILAN UNIVERSITY   (Israel)

^b TEL AVIV SOURASKY MEDICAL CENTER   (Israel)

^c UNIVERSITY OF POTSDAM   (Germany)

Author keywords

Delay; Nonstationarity; Synchronization; Synchronization decay; Tremor

Indexed keywords

BIOELECTRIC POTENTIALS; DISEASES;

DELAY; NONSTATIONARITY; SYNCHRONIZATION DECAY; TREMOR;

SYNCHRONIZATION;

EID: 33646175283     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2005.10.033     Document Type: Article

References (21)

1. A.S. Pikovsky, M.G. Rosenblum, J. Kurths, Synchronization-A Universal Concept in Nonlinear Science, Cambridge, 2001.
2. Boccaletti S., Kurths J., Osipov G., Valladares D.L., and Zhou C.S. Phys. Rep. 366 (2001) 1
3. Pikovsky A.S., Rosenblum M.G., Osipov G.V., and Kurths J. Physica D 104 (1997) 219
4. M.G. Rosenblum, A.S. Pikovsky, J. Kurths, C. Schäfer, P.A. Tass, Phase synchronization: from theory to data analysis, in: F. Moss, S. Gielen (Eds.), Handbook of Biological Physics, vol. 4, Neuro-informatics, Elsevier, Amsterdam, 2001, pp. 279-321 (Chapter 9).
5. Tass P., Rosenblum M.G., Weule J., Kurths J., Pikovsky A., Volkmann J., Schnitzler A., and Freund H.-J. Phys. Rev. Lett. 81 3291 (1998)
6. Schaefer C., Rosenblum M.G., Kurths J., and Abel H.H. Nature 392 (1998) 239
7. Stefanovska A., Haken H., McClintock P.V.E., Hožič M., and Ribarič S. Phys. Rev. Lett. 85 (2000) 4831
8. Kotani K., Takamasu K., Ashkenazy Y., Stanley H.E., and Yamamoto Y. Phys. Rev. E 65 (2001) 519
9. Rybsky D., Havlin S., and Bunde A. Physica A 320 (2003) 601
10. Moshel S., Liang J., Caspi A., Engbert R., Kliegl R., Havlin S., and Zivotofsky A.Z. Ann. NY Acad. Sci. 1039 (2005) 484
11. Gabor D. J. IEEE London 93 (1946) 429
12. C.H. Hugenii (Huygens), Horologium Oscillatorium (1673), Apud F. Muguet, Parisiis, France; English Translation: Iowa State University Press, Ames, 1986.
13. Cimponeriu L., Rosenblum M., and Pikovsky A. Phys. Rev. E 70 (2004) 046213
14. The correction mentioned is proved to exist for a different kind of synchronization index.
15. Otnes R., and Enochson L. Digital Time Series Analysis (1972), Wiley, New York
16. i = 0 for all bins outside the ε{lunate}-zone.
17. Shannon C.E. Bell System Technical J. 27 (1948) 379
18. Bergman H., and Deuschl G. Movement Disord. 17 Suppl. 3 (2002) S28
19. Sapir N., Karasik R., Havlin S., Simon E., and Hausdorff J.M. Phys. Rev. E 67 (2003) 031903
20. Raz A., Vaadia E., and Bergman H. Movement Disord. 20 22 (2000) 8559
21. Here, we modified τ once in each cycle, giving it 10 different discrete values alternately. The reason for this perturbing strategy is that the phase is a zero Lyapunov parameter, and therefore its dynamic is too sensitive to frequent noise.