Effective deterministic models for chaotic dynamics perturbed by noise

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

Volumn 55, Issue 5, 1997, Pages 5234-5247

  Jaeger, Lars ^a   Kantz, Holger ^a  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001637554     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.5234     Document Type: Article

References (36)

1. C. Grebogi, St. Hammel, J. Yorke and T. Sauer, Phys. Rev. Lett.65, 1527 (1990);
2. S M. Hammel, J M. Yorke and C. Grebogi, J. Compl.3, 136 (1987).
3. J C. Sommerer, E. Ott and C. Grebogi, Phys. Rev. A43, 1754 (1991).
4. P. Grassberger, R. Hegger, H. Kantz, C. Schaffrath and T. Schreiber, CHAOS3, 127 (1993).
5. J D. Farmer and J J. Sidorowich, Physica D47, 373 (1991).
6. M. Davies, Int. J. Bifurc. Chaos3, 113 (1992);
7. M. Davies, Physica D79, 174 (1994).
8. L. Jaeger and H. Kantz, CHAOS6, 440 (1996);
9. H. Kantz and L. Jaeger, Physica D (to be published).
10. For an excellent overview, see R. Bowen, On Axiom A systems, CBMS Regional Conference Series in Mathematics Vol. 35 (American Mathematical Society, Providence, RI, 1970);
11. B V. Anosov, Proc. Steklov Inst. Math.90, 1 (1967);
12. R. Bowen, J. Diff. Eq.18, 333 (1975).
13. L. Jaeger and H. Kantz, Physica D (to be published).
14. H E. Nusse and J A. Yorke, Commun. Math. Phys.114, 363 (1988).
15. T. Sauer, J. Yorke and M. Casdagli, J. Stat. Phys.65, 579 (1991).
16. M. Hénon, Commun. Math. Phys.50, 69 (1976).
17. P. Grassberger, H. Kantz and U. Mönig, Phys. Lett.113A, 235 (1985);
18. J. Phys. A22, 5217 (1989).
19. P. Grassberger and I. Procaccia, Phys. Rev. Lett.50, 346 (1983);
20. P. Grassberger and I. Procaccia, Physica D9, 189 (1983).
21. H. Kantz, Phys. Rev. E49, 5091 (1994).
22. Y. Kifer, Theory of Random Transformations (Birkhäuser, Boston, 1986).
23. L. Arnold, in Dynamical Systems, edited by R. Johnson, Lecture Notes in Mathematics Vol. 1609 (Springer, Berlin, 1995).
24. A. Maritan and J R. Banavar, Phys. Rev. Lett.72, 1451 (1994);
25. G. Malescio, Phys. Lett. A218, 25 (1996).
26. V. Loreto, G. Paladin and A. Vulpiani, Phys. Rev. E53, 2087 (1996);
27. G. Paladin, M. Serva and A. Vulpiani, Phys. Rev. Lett.74, 66 (1995).
28. A. Wolf, J B. Swift, H L. Swinney and J A. Vastano, Physica D16, 285 (1985).
29. A N. Kolmogorov, IRE Trans. Inf. Theory1, 102 (1956).
30. P. Gaspard and X J. Wang, Phys. Rep.235, 291 (1993).
31. H. Kantz, Phys. Lett. A185, 77 (1994).
32. R. Gencay and W D. Dechert, Physica D59, 142 (1992).
33. F T. Arecchi, W. Gadomski and R. Meucci, Phys. Rev. A34, 1617 (1985);
34. M. Ciofini, R. Meucci and F T. Arecchi, Phys. Rev. E52, 94 (1995).
35. L. Jaeger, H. Kantz, R. Hegger, H. Beige, and M. Diestelhorst (unpublished).
36. G D. Szpiro, Physica D65, 289 (1993).