When noise decreases deterministic diffusion

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

Volumn 59, Issue 3, 1999, Pages 2872-2879

  Wackerbauer, Renate ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001140979     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.2872     Document Type: Article

References (21)

1. I. Dayan, M. Gitterman, and G.H. Weiss, Phys. Rev. A 46, 757 (1992).
2. R.N. Mantegna, and B. Spagnolo, Phys. Rev. Lett. 76, 563 (1996).
3. F. Apostolico, L. Gammaitoni, F. Marchesoni, and S. Santucci, Phys. Rev. E 55, 36 (1997).
4. R. Wackerbauer, Phys. Rev. E 52, 4745 (1995).
5. N.V. Agudov, Phys. Rev. E 57, 2618 (1998).
6. R. Wackerbauer, Phys. Rev. E 58, 3036 (1988).
7. S. Grossmann and S. Thomae, Phys. Lett. A 97, 263 (1983)
8. T. Geisel and S. Thomae, Phys. Rev. Lett. 52, 1936 (1984).
9. R. Klages and J.R. Dorfman, Phys. Rev. Lett. 74, 387 (1995).
10. R. Artuso, Physica D 76, 1 (1994).
11. C.R. Doering, W. Horsthemke, and J. Riordan, Phys. Rev. Lett. 72, 2984 (1994)
12. R. Bartussek, P. Hänggi, and J.G. Kissner, Europhys. Lett. 28, 459 (1994).
13. T. Geisel and J. Nierwetberg, Phys. Rev. Lett. 48, 7 (1982).
14. M.F. Shlesinger, G.M. Zaslavsky, and J. Klafter, Nature (London) 363, 31 (1993), and references therein.
15. G. Casati, B.V. Chirikov, J. Ford, and F.M. Izrailev, Lect. Notes Phys. 93, 334 (1979).
16. P.W. Anderson, Phys. Rev. 109, 1492 (1958).
17. J.L. Skinner, J. Phys. Chem. 98, 2503 (1994), and references therein.
18. P. Allegrini, P. Grigolini, and B.J. West, Phys. Rev. E 54, 4760 (1996).
19. Let (Formula presented) be the average gain of iteration steps by a single negative noise event acting in (Formula presented) The probability for (Formula presented) negative perturbation is (Formula presented) since it is caused by a noise sequence (Formula presented) Thus, the total gain of iterations by negative noise events is given by (Formula presented) e.g., it is just the gain of iterations for one single negative perturbation.
20. To be exact, for maximizing the mean residence time (Formula presented) the product of (Formula presented) and (Formula presented) should be optimized with respect to (Formula presented) However, a usually strong decrease of (Formula presented) near (Formula presented) dominates the optimization, which is why (Formula presented) is still a good approximation.
21. R. Wackerbauer (unpublished).