Local box-counting to determine fractal dimension of high-order chaos

International Journal of Modern Physics C

Volumn 11, Issue 8, 2000, Pages 1519-1526

  Osaka, Motohisa ^a   Ito, Nobuyasu ^b  

^a NIPPON MEDICAL SCHOOL   (Japan)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

Chaos; Complexity; Dimension; Fractal; Nonlinear Dynamics; Time Delay Equation

Indexed keywords

EID: 0034561080     PISSN: 01291831     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129183100001474     Document Type: Article

References (20)

1. M. Casdagli, Physica D 35, 335 (1989).
2. G. Sugihara and R. M. May, Nature 344, 734 (1990).
3. D. T. Kaplan and L. Glass, Physica D 64, 431 (1993).
4. K. H. Chon, J. K. Kanters, R. J. Cohen, and N.-H. Holstein-Rathlou, Physica D 99, 471 (1997).
5. P. E. Rapp, I. D. Zimmerman, A. M. Albano, G. C. de Guzman, and N. N. Greenbaum, Phys. Lett. A 110, 335 (1985).
6. A. L. Hodgkin and A. F. Huxley, J. Physiol. 117, 500 (1952).
7. J. Guckenheimer and I. S. Labouriau, Bull. Math. Biol. 55, 937 (1993).
8. D. DiFranasco and D. Noble, Philos. Trans. R. Soc. Lond. B 307, 353 (1988).
9. D. Noble and G. Bett, Cardiovasc. Res. 27, 1701 (1993).
10. H. D. I. Abarbanel, Analysis of Observed Chaotic Data (Springer, New York, 1996).
11. H.-O. Peitgen, H. Jurgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science (Springer, New York, 1992).
12. L. S. Liebovitch and T. Toth, Phys. Lett. A 141, 386 (1989).
13. M. Sano and Y. Sawada, Phys. Rev. Lett. 55, 1082 (1985).
14. M. C. Mackey and L. Glass, Science 197, 287 (1977).
15. J. D. Farmer, Physica D 4, 366 (1982).
16. P. Grassberger and I. Procaccia, Physica D 9, 189 (1983).
17. H. D. I. Abarbanel and M. B. Kennel, Phys. Rev. E 47, 3057 (1993).
18. A. M. Fraser and H. L. Swinney, Phys. Rev. A 33, 1134 (1986).
19. A. S. Weigend and N. A. Gershenfeld, to appear in Time Series Prediction, eds. A. S. Weigend and N. A. Gershenfeld (Addison-Wesley, MA, 1994).
20. K. Ikeda and K. Matsumoto, Physica D 29, 223 (1987).