The necessity for a time local dimension in systems with time-varying attractors

Physica A: Statistical Mechanics and its Applications

Volumn 236, Issue 3-4, 1997, Pages 363-375

  Saermark, K ^a   Ashkenazy, Y ^b   Levitan, J ^b,c   Lewkowicz, M ^b,c  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b BAR ILAN UNIVERSITY   (Israel)

^c ARIEL UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; CHAOS THEORY; DIFFERENTIAL EQUATIONS; ELECTROENCEPHALOGRAPHY; TIME SERIES ANALYSIS;

MAGNETOENCEPHALOGRAPHY; TIME-VARYING ATTRACTORS;

NONLINEAR SYSTEMS;

EID: 0031095858     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(96)00367-6     Document Type: Article

References (29)

1. A. Babloyantz, C. Nicolis and M. Salazar, Phys. Lett. A 111 (1985) 152; A. Babloyantz and A. Destexhe, Proc. Natl. Acad. Sci. USA 83 (1986) 3513-3517.
2. A. Babloyantz, C. Nicolis and M. Salazar, Phys. Lett. A 111 (1985) 152; A. Babloyantz and A. Destexhe, Proc. Natl. Acad. Sci. USA 83 (1986) 3513-3517.
3. E. Basar, ed., Chaos in the Brain (Springer, Berlin, 1990).
4. G. Mayer-Kress, F.E. Yates, L. Benton, M. Keidel, W.S. Tirsch and S.J. Poepple, Math. Biosci. 90 (1988) 155.
5. K. Saermark, J. Lebech, C.K. Bak and A. Sabers, in: Springer Series in Brain Dynamics, 2 eds. E. Basar and T.H. Bullock (Springer, Berlin, 1989) p. 149.
6. A. Meyer-Lindenberg and B. Gallhofer, Regional analysis of deterministic chaos in schizophrenia, preprint.
7. G. Mayer-Kress, C. Barczys and W.J. Freeman, in: Mathematical Approaches to Brain Functioning Diagnostics, eds. I. Dvorak and A.V. Holden (Manchester University Press, Manchester, 1991) p. 315.
8. D.E. Sigeti, Physica D 82 (1995) 136.
9. U. Frisch and R. Morf, Phys. Rev. A 23 (1981) 2673.
10. T. Elbert, W.J. Ray, Z.J. Kowalick, J.E. Skinner, K.E. Graf and N. Birnbaumer, Physiol. Rev. 74 (1994) 1.
11. H.D.I. Abarbanel, R. Brown, J.J. Sidorowich and L.S. Tsimring, Rev. Mod. Phys. 65 (1993) 1331.
12. G. Mayer-Kress, Integrative Physiol. Behavioral Sci. 29 (1994) 205.
13. Y. Ashkenazy, M.Sc. Thesis, Bar-Ilan University, Ramat-Gan, Israel (1995).
14. L.A. Smith, Phys. Lett. A 133 (1988) 283.
15. J. Theiler, Phys. Rev. A 41 (1990) 3038.
16. D. Ruelle, Proc. Roy Soc. A 427 (1990) 241.
17. K. Saermark, K.B. Mikkelsen and E. Basar, in: Induced Rhythms of the Brain, eds. E. Basar and T. Bullock (Birkhauser, Basel, 1992) pp. 129-145.
18. Y. Ashkenazy, L.P. Horowitz, J. Levitan, M. Lewkowicz and Y. Rothschild, Phys. Rev. Lett. 75 (1995) 1070.
19. M. Ding, C. Grebogi, E. Ott, T. Sauer and J.A. Yorke, Physica D 69 (1993) 404.
20. P. Grassberger and I. Procaccia, Physica D 9 (1983) 189.
21. J.-P. Eckmann and D. Ruelle, Physica D 56 (1992) 185.
22. F. Takens, in: Dynamical Systems and Turbulence, eds. D. Rand and L.S. Young (Springer, New York, 1981).
23. K. Pawelzik and H.G. Schuster, Phys. Rev. A 35 (1987) 481.
24. Z.J. Kowalick and T. Elbert, in: Biomagnetism: Fundamental research and Clinical Implications, eds. C. Baumgartner et al. (Elsevier, Amsterdam, 1995).
25. A. Renyi, Probability Theory (North-Holland, Amsterdam, 1970).
26. I. Dvorak and J. Klaschka, Phys. Lett. A 145 (1990) 225.
27. A. Wolf, J.B. Swift, H.L. Swinney and J.A. Vastano, Physica D 16 (1985) 285.
28. G.L. Baker and J.P. Gollub, Chaotic Dynamics (Cambridge Univeristy Press, Cambridge, 1990).
29. Y. Ashkenazy, J. Levitan and M. Lewkowicz, preprint.