Detecting the onset of bifurcations and their precursors from noisy data

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

Volumn 61, Issue 5, 2000, Pages 4848-4853

  Omberg, Larsson ^a,b   Dolan, Kevin ^a   Neiman, Alexander ^a   Moss, Frank ^a  

^a UNIVERSITY OF MISSOURI ST LOUIS   (United States)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICAL SYSTEMS; STOCHASTIC SYSTEMS;

NOISY DATA; PERIOD DOUBLING BIFURCATION; PERIODIC MOTION; STOCHASTIC DYNAMICAL SYSTEM;

BIFURCATION (MATHEMATICS);

EID: 0000443952     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.4848     Document Type: Article

References (25)

1. L. Arnold, Random Dynamical Systems (Springer, Berlin, 1998).
2. M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems (Springer, Berlin, 1984).
3. R. Graham, in Noise in Nonlinear Dynamical Systems, edited by F. Moss and P. V. E. McClintock (Cambridge University Press, Cambridge, England, 1989).
4. A. Neiman, V. Anishchenko, and J. Kurths, Phys. Rev. E 49, 3801 (1994).
5. A. Neiman, U. Feudel, and J. Kurths, J. Phys. A 28, 2471 (1995).
6. L. Fronzoni, R. Mannella, P. V. E. McClintock, and F. Moss, Phys. Rev. A 36, 834 (1987).
7. C. Meunier and A. D. Verga, J. Stat. Phys. 50, 345 (1988).
8. K. Wiesenfeld, J. Stat. Phys. 38, 1071 (1985).
9. A. Neiman, P. I. Saparin, and L. Stone, Phys. Rev. E 56, 270 (1997).
10. R. Benzi, A. Sutera, and A. Vulpiani, J. Phys. A 14, L453 (1981).
11. R. Benzi, G. Parisi, A. Sutera, and A. Vulpiani, Tellus 34, 10 (1982).
12. K. Wiesenfeld and F. Moss, Nature (London) 373, 33 (1995).
13. T. Kim and E. H. Abed, IEEE Trans. Circuits Syst., I (in press).
14. W. L. Ditto, M. L. Spano, and J. F. Lindner, Physica D 86, 198 (1995).
15. A. Garfinkle, M. L. Spano, W. L. Ditto, and J. N. Weiss, Science 257, 1230 (1992).
16. H. A. Braun, K. Schäfer, K. Voigt, R. Peters, F. Bretschneider, X. Pei, L. Wilkens, and F. Moss, J. Comput. Neurosci. 4, 335 (1997).
17. H. A. Braun, M. Dewald, K. Schäfer, K. Voigt, X. Pei, K. Dolan, and F. Moss, J. Comput. Neurosci. 7, 17 (1999).
18. K. Dolan, W. Witt, M. L. Spano, A. Neiman, and F. Moss, Phys. Rev. E 59, 5235 (1999).
19. D. Pierson and F. Moss, Phys. Rev. Lett. 75, 2124 (1995).
20. X. Pei and F. Moss, Nature (London) 379, 618 (1996).
21. X. Pei and F. Moss, Int. J. Neural Syst. 7, 429 (1996).
22. O. E. Rössler, Phys. Lett. A 57, 397 (1976).
23. S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, NY, 1994).
24. L. P. Shilnikov, A. L. Shilnikov, D. V. Turaev, and L. O. Chua, Methods of Qualitative Theory in Nonlinear Dynamics. Part I (World Scientific, Singapore, 1998).
25. P. R. Bevington, in Data Reduction and Error Analysis (McGraw-Hill, New York, 1969), pp. 48–49.