Effects of the low frequencies of noise on on-off intermittency

Journal of Statistical Physics

Volumn 123, Issue 4, 2006, Pages 909-927

  Aumaître, Sébastien ^a,b   Mallick, Kirone ^c   Pétrélis, François ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b HAVERFORD COLLEGE   (United States)

^c CEA SACLAY   (France)

Author keywords

Dynamical systems; Effect of noise on bifurcations; On off intermittency; Stochastic dynamics

Indexed keywords

EID: 33747632719     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-006-9116-9     Document Type: Article

References (31)

1. N. G. van Kampen, Physics Reports 24, 171 (1976).
2. M. Neufeld and R. Friedrich, Phys. Rev. E 51, 2033 (1995).
3. D. Sweet, E. Ott, J. M. Finn, T. M. Antonsen Jr. and D. P. Lathrop, Phys. Rev. E 63, 066211 (2001);
4. D. Sweet, E. Ott, T. M. Antonsen Jr., D. P. Lathrop and J. M. Finn, Phys. Plasma 8, 1944 (2001);
5. S. Fauve and F. Pétrélis, The dynamo effect, in Peyresq Lectures on Nonlinear Phenomena, Vol. II, J.-A. Sepulchre, ed. (World Scientific, Singapour, 2003), pp. 1-66.
6. R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New-York, 1963).
7. T. Kawakubo, S. Kabashima and Y. Tsuchiya, Prog. Theor. Phys. Supp. 64, (1978).
8. A. Schenzle and H. Brand, Phys. Rev. A 20, 1628 (1979);
9. R. Graham and A. Schenzle, Phys. Rev. A 26, 1676 (1982).
10. W. Horsthemke and R. Lefever, Noise-Induced Transitions (Springer-Verlag, 1984).
11. T. Yamada and H. Fujisaka, Prog. Theor. Phys. 76, 582 (1986);
12. H. Fujisaka, H. Ishii, M. Inoue and T. Yamada, Prog. Theor. Phys. 76, 1198 (1986);
13. N. Platt, E. A. Spiegel and C. Tresser, Phys. Rev. Lett. 70(3), 279-282 (1993).
14. P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy and B. D. Lee, Phys. Rev. Lett. 73, 1095 (1994);
15. T. John, R. Stannarius and U. Behn, Phys. Rev. Lett. 83, 749 (1999);
16. D. L. Feng, C. X. Yu, J. L. Xie and W. X. Ding, Phys. Rev. E 58, 3678 (1998);
17. F. Rödelspreger, A. Cenys and H. Benner, Phys. Rev. Lett. 75, 2594 (1995).
18. S. Aumaître, F. Pétrélis and K. Mallick, Phys. Rev. Lett. 95, 064101 (2005).
19. M. Lücke and F. Schanck, Phys. Rev. Lett. 54, 1465 (1985).
20. K. Mallick and P. Marcq, Euro. Phys. J. B 38, 99 (2004).
21. F. Pétrélis and S. Aumaître, Eur. Phys. J. B 34, 281-284 (2003).
22. N. G. van Kampen, Stochastic Process in Physics Chemistry (North-Holland, Amsterdam, 1992).
23. A. Teubel, U. Beim and A. Kühnel, Zeitschrift für Physik B-Condensed Matter 71, 393-402 (1988);
24. I. Bena, C. Van Den Broeck, R. Kawai and K. Lindenberg, Phys. Rev. E 66, 045603(R) (2002). We are indebted to C. Van den Broeck for suggesting us the calculation presented in part 2.3.
25. B. L. Sawford, Phys. Fluids A 3, 1577 (1991).
26. L. Schimansky-Geier and Ch. Zülicke, Z. Phys. B 79, 451-460 (1990).
27. This expression corrects a misprint for M defined in ref. 10.
28. M. Lücke, Noise in nonlinear dynamical systems, Vol 2, F. Moss & P. V E. McClintock, eds. (Cambridge University Press, 1989).
29. J. F. Heagy, N. Platt and S. M. Hammel, Phys. Rev. E 49, 1140 (1994).
30. A. Čenys, A. N. Anagnopoulos and G. L. Bleris, Phys Lett. A 224, 346 (1997).
31. E. Lorenz, J. Atmos. Sci. 20, 244 (1963).