Asymptotically stable phase synchronization revealed by autoregressive circle maps

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 5, 2000, Pages 6376-6382

  Drepper, F R ^a  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; FOURIER TRANSFORMS; LYAPUNOV METHODS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PHASE SPACE METHODS; REGRESSION ANALYSIS; STATE SPACE METHODS; TIME SERIES ANALYSIS;

AUTOREGRESSIVE CIRCLE MAPS; POLAR ANGLES;

MOLECULAR DYNAMICS;

EID: 0034316685     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.6376     Document Type: Article

References (31)

1. F. Takens, in Dynamical Systems and Turbulence, edited by D. Rand and L. S. Young, Lecture Notes in Mathematics Vol. 898 (Springer, Berlin, 1981).
2. N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Phys. Rev. Lett. 45, 712 (1980).
3. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 1997).
4. D. Gabor, J. IEE London 93, 429 (1946).
5. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
6. M. G. Rosenblum, J. Kurths, A. Pikovsky, C. Schäfer, P. Tass, and H.-H. Abel, IEEE Eng. Med. Biol. Mag. 17, 46 (1998).
7. P. Tass, M. G. Rosenblum, J. Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, Phys. Rev. Lett. 81, 3291 (1998).
8. M. Casdagli, Physica D 35, 335 (1989).
9. F. R. Drepper, R. Engbert, and N. Stollenwerk, Ecol. Mod. 75/76, 171 (1994).
10. Christiaan Huygens, in Ostwald’s Klassiker der exakten Wissenschaften, edited by A. Heckscher and A. von Öettingen (Engelmann, Leipzig, 1913).
11. R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New York, 1963).
12. H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69, 32 (1983).
13. V. S. Afraimovich, N. N. Verichev, and M. I. Rabinovich, Radiophys. Quantum Electron. 29, 795 (1986).
14. L. M. Pecora and T. L. Caroll, Phys. Rev. Lett. 64, 821 (1990).
15. N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel, Phys. Rev. E 51, 980 (1995).
16. L. Kocarev and U. Parlitz, Phys. Rev. Lett. 76, 1816 (1996).
17. S. J. Schiff, P. So, T. Chang, R. E. Burke, and T. Sauer, Phys. Rev. E 54, 6708 (1996).
18. C. Schäfer, M. G. Rosenblum, J. Kurths, and H.-H. Abel, Nature (London) 392, 239 (1998).
19. C. Ludwig, Arch. Anat. Physiol. 13, 242 (1847).
20. C. T. M. Davies and J. M. M. Neilson, J. Appl. Physiol. 22, 947 (1967).
21. J. A. Hirsch and B. Bishop, Am. J. Physiol. 241, H620 (1981).
22. H. P. Koepchen, in Mechanisms of Blood Pressure Waves, edited by K. Miyakawa, H. P. Koepchen, and C. Polosa (Springer, Berlin, 1984).
23. M. P. Gilbey, D. Jordan, D. W. Richter, and K. M. Spyer, J. Physiol. (London) 365, 65 (1984).
24. D. L. Eckberg, Y. T. Kifle, and V. L. Roberts, J. Physiol. (London) 304, 489 (1980).
25. K. Suder, F. R. Drepper, M. Schiek, and H.-H. Abel, Am. J. Physiol. 275, H1092 (1998).
26. J. Arnhold, P. Grassberger, K. Lehnertz, and C. E. Elger, Physica D 134, 419 (1999)
27. R. Q. Quivoga, J. Arnold, and P. Grassberger, Phys. Rev. E 61, 5142 (2000).
28. E. v. Holst, Ergeb. Physiol. 42, 228 (1939).
29. M. Schiek, Ph.D. thesis, RWTH Aachen, 1998.
30. A. Neiman, A. Silchenco, V. Anishchenko, and L. Schimanski-Geier, Phys. Rev. E 58, 7118 (1998).
31. M. Schiek, F. R. Drepper, R. Engbert, H.-H. Abel, and K. Suder, in Nonlinear Analysis of Physiological Data, edited by K. Kantz, J. Kurths, and G. Mayer-Kress (Springer, Berlin, 1998).