A new criterion to distinguish stochastic and deterministic time series with the Poincaŕ section and fractal dimension

Chaos

Volumn 19, Issue 1, 2009, Pages

  Golestani, Abbas ^a   Jahed Motlagh, M R ^a   Ahmadian, K ^a   Omidvarnia, Amir H ^b   Mozayani, Nasser ^a  

^a IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

^b UNIVERSITY OF TEHRAN   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ANATOMY AND HISTOLOGY; ANIMAL; BIOPHYSICS; FRACTAL ANALYSIS; HUMAN; IRIS; NONLINEAR SYSTEM; NORMAL DISTRIBUTION; PHYSIOLOGY; PROCEDURES; SIGNAL PROCESSING; STATISTICAL MODEL; STATISTICS; TIME;

ALGORITHMS; ANIMALS; BIOPHYSICS; FRACTALS; HUMANS; IRIS; MODELS, STATISTICAL; NONLINEAR DYNAMICS; NORMAL DISTRIBUTION; SIGNAL PROCESSING, COMPUTER-ASSISTED; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 63849318059     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3096413     Document Type: Article

References (36)

1. J. Hubbard and B. West, Differential Equations: A Dynamical Systems Approach: Ordinary Differential Equations (Springer, Berlin, 1991), Vol. 5.
2. P. Grassberger, T. Schreiber, and C. Schaffrath, Int. J. Bifurcation Chaos Appl. Sci. Eng. 0218-1274 10.1142/S0218127491000403 1, 521 (1991).
3. A. H. Omidvarnia and A. Nasrabadi, Fractals 16, 129 (2008). 0218-348X
4. A. Brandstater, J. Swift, and H. L. Swinney, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.51.1442 51, 1442 (1983).
5. P. Berge, Y. Pomeau, and C. Vidal, " Order within Chaos: Towards a Deterministic Approach to Turbulence (Wiley, New York, 1984).
6. A. R. Osborne and A. Provenzale, Physica 35D, 357 (1989). 0031-8914
7. J. Theiler, Phys. Lett. A 0375-9601 10.1016/0375-9601(91)90651-N 155, 480 (1991).
8. N. P. Greis and H. S. Greenside, Phys. Rev. A 1050-2947 10.1103/PhysRevA.44.2324 44, 2324 (1991).
9. K. Najarian, K. Gopalakrishnan, and R. H. Zadeh, Int. J. Bioinformatics Research and Applications (IJBRA) 1, 102 (2005). 1050-2947
10. T. Higuchi, Physica D 0167-2789 10.1016/0167-2789(88)90081-4 31, 277 (1988).
11. T. Higuchi, Physica D 0167-2789 10.1016/0167-2789(90)90039-R 46, 254 (1990).
12. L. Telesca, Chaos, Solitons Fractals 18, 385 (2003). 0960-0779
13. W. Klonowski, E. Olejarczyk, and R. Stepien, Signal processing for functional analysis of protein mutants, Attractors, Signals, and Synergetics, Frontiers of Non-linear Dynamics (Pabst Science, Lengerich, 2002), Vol. 1, pp. 553-560.
14. A. Anier, T. Lipping, S. Melto, and S. Hovilehto, Proceedings of the 26th Annual International Conference of the IEEE IEMBS APOS'04, 2004 (unpublished), Vol. 1, pp. 526-529.
15. A. Accardo, M. Affinito, and M. Carrozzi, Biol. Cybern. 0340-1200 10.1007/s004220050394 77, 339 (1997).
16. W. Klonowski, Chaos, Solitons Fractals 14, 1379 (2002). 0960-0779
17. W. Klonowski, Nonlinear Biomed. Phys. 1, 5 (2007). 1753-4631
18. M. Moradi, P. Abolmaesumi, and A. Phillip, Proceedings of the 28th Annual International Conference of the IEEE EMBS APOS'06, 2006 (unpublished), pp. 2400-2403.
19. A. Basu, Project in School of Electrical and Computer Engineering Georgia Institute of Technology, Atlanta, GA, 2007.
20. N. B. Tufillaro, Poincare Map, 1997.
21. F. Takens, Dynamical Systems and Turbulence, Lecture Notes in Mathematics, Vol. 898 (Springer, Berlin, 1981) p. 366.
22. S. Smale, Bull. Am. Math. Soc. 0002-9904 10.1090/S0002-9904-1967-11798-1 73, 747 (1967).
23. M. Branson, Proceedings of the AIAA Space, 2006 (unpublished).
24. J. C. Sprott, Chaos and Time Series Analysis (Oxford University Press, Oxford, 2003).
25. G. Marsaglia and A. Zaman, Ann. Appl. Probab. 1, 462 (1991). 1050-5164
26. G. Marsaglia and W. W. Tsang, J Stat. Software 5, 1 (2000). 1050-5164
27. E. Ott, Chaos in Dynamical System (Cambridge University Press, New York, 2002).
28. E. N. Lorenz, J. Atmos. Sci. 0022-4928 10.1175/1520-0469(1963) 020<0130:DNF>2.0.CO;2 20, 130 (1963).
29. O. E. Rössler, Phys. Lett. 0370-2693 10.1016/0375-9601(76)90101-8 57A, 397 (1976).
30. P. Grassberger and I. Procaccia, Physica 9D, 189 (1983). 0031-8914
31. B. van der Pol and J. van der Mark, Nature (London) 0028-0836 10.1038/120363a0 120, 363 (1927).
32. R. Fitzhugh, Biophys. J. 0006-3495 10.1016/S0006-3495(61)86902-6 1, 445 (1961).
33. R. P. Wildes, Proc. IEEE 85, 9 (1997). 0006-3495
34. F. H. Adler, Physiology of the Eye (Mosby, St. Louis, MO, 1965).
35. National Laboratory of Pattern Recognition, Chinese Academy of Sciences, available at http://www.sinobiometrics.com.
36. C. Merkwirth, U. Parlitz, and I. Wedekind, W. Lauterborn, TSTOOL, Version, 1.11, 2002, downloadable from http://www.physik3.gwdg.de/tstool/index. html.