On a quantitative method to analyze dynamical and measurement noise

Europhysics Letters

Volumn 61, Issue 4, 2003, Pages 466-472

  Siefert, M ^a   Kittel, A ^a   Fribdrich, R ^b   Peinke, J ^a  

^a UNIVERSITY OF OLDENBURG   (Germany)

^b UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037325324     PISSN: 02955075     EISSN: None     Source Type: Journal    
DOI: 10.1209/epl/i2003-00152-9     Document Type: Article

References (23)

1. SCHREIBER T. and KANTZ H., Nonlinear Time Series Analysis (Cambridge University Press) 1997.
2. ABARBANEL H. D. I., Analysis of Observed Chaotic Data (Springer-Verlag, Berlin) 1996.
3. HILBORN R. C. and TUFILLARO N. B., Am. J. Phys., 65 (1997) 822.
4. SIEGERT S., FRIEDRICH R. and PEINKE J., Phys. Lett. A, 243 (1998) 275.
5. BORLAND L. and HAKEN H., Z. Phys. B, 81 (1992) 95.
6. BORLAND L. and HAKEN H., Ann. Phys. (Leipzig), 1 (1992) 452.
7. KLIMONTOVICH Y. L., Int. J. Bifurcat. Chaos, 3 (1993) 119.
8. STARK M. R. J., BROOMHEAD D. S., DAVIES M. E. and HUKE J., Nonlin. Anal-Theory Methods Applicat., 30 (1997) 5303.
9. MULDOON M. R., BROOMHEAD D. S., HUKE J. P. and HEGGER R., Dynam. Stabil. Syst., 13 (1998) 175.
10. HEALD J. P. M. and STARK J., Phys. Rev. Lett., 84 (2000) 2366.
11. RENNER CH., PEINKE J. and FRIEDRICH R., J. Fluid Mech., 433 (2001) 383.
12. FRIEDRICH R., SIEGERT S., PEINKE J., LÜCK ST., SIEFERT M., LINDEMANN M., RAETHJEN J., DEUSCHL G. and PFISTER G., Phys. Lett. A, 271 (2000) 217.
13. GRADISEK J., SIEGERT S., FRIEDRICH R. and GRABEC I., Phys. Rev. E, 62 (2000) 3146.
14. KOLMOGOROV A. N., Math. Ann., 140 (1931) 415.
15. MOYAL J. E., J. R. Stat. Soc., 11 (1949) 195.
16. Here we used 77.5 samples per mean recurrent time, corresponding to a sampling rate of 66 kHz. Problems arising for large At are discussed in [23].
17. RISKEN H., The Fokker-Planck Equation (Springer-Verlag, Berlin) 1984.
18. (2) to higher order terms in Δt is given in [19, 20].
19. RAGWITZ M. and KANTZ H., Phys. Rev. Lett., 87 (2001) 254501.
20. FRIEDRICH R., RENNER CH., SIEFERT M. and PEINKE J., arXiv:physics/0203005.
21. SHINRIKI M., YAMAMOTO M. and MORI S., Proc. IEEE, 69 (1981) 394.
22. Investigations without this averaging leads to similar results.
23. TIMMER J., Chaos, Solitons Fractals, 11 (2000) 2571.