Phase diagram of the random frequency oscillator: The case of Ornstein-Uhlenbeck noise

Physica D: Nonlinear Phenomena

Volumn 221, Issue 1, 2006, Pages 72-83

  Mallick, Kirone ^a   Peyneau, Pierre Emmanuel ^a  

^a CEA SACLAY   (France)

Author keywords

Colored noise; Fokker Planck equations; Random processes; Stochastic analysis methods

Indexed keywords

APPROXIMATION THEORY; FREQUENCY MODULATION; LYAPUNOV METHODS; PHASE DIAGRAMS; RANDOM PROCESSES; SPURIOUS SIGNAL NOISE;

COLORED NOISE; FOKKER-PLANCK EQUATIONS; ORNSTEIN-UHLENBECK NOISE; STOCHASTIC ANALYSIS METHODS;

OSCILLATORS (ELECTRONIC);

EID: 33747789049     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2006.07.013     Document Type: Article

References (50)

1. van Kampen N.G. Stochastic Processes in Physics and Chemistry (1992), North-Holland, Amsterdam
2. Gardiner C.W. Handbook of Stochastic Methods (1994), Springer-Verlag, Berlin
3. Anishchenko V.S., Astakhov V.V., Neiman A.B., Vadivasova T.E., and Schimansky-Geier L. Nonlinear Dynamics of Chaotic and Stochastic Systems (2002), Springer-Verlag, Berlin
4. Horsthemke H., and Lefever R. Noise Induced Transitions (1984), Springer-Verlag, Berlin
5. Berthet R., Residori S., Roman B., and Fauve S. Phys. Rev. Lett. 33 (2002) 557
6. Pétrélis F., and Aumaître S. Eur. Phys. J. B 34 (2003) 281
7. Muñoz M.A. Nonequilibrium phase transitions and multiplicative noise. In: Korutcheva E., and Cuerno R. (Eds). Advances in Condensed Matter and Statistical Mechanics (2004), Nova Science Publishers. cond-mat/0303650
8. Pikovsky A., Rosenblum M., and Kurths J. Synchronization, A Universal Concept in Nonlinear Sciences (2001), Cambridge University Press
9. Lücke M., and Schank F. Phys. Rev. Lett. 54 (1985) 1465
10. Lücke M. In: Moss F., and McClintock P.V.E. (Eds). Noise in Dynamical Systems. Theory of Noise-induced Processes in Special Applications vol. 2 (1989), Cambridge University Press, Cambridge
11. Ebeling W., Herzel H., Richert R., and Schimansky-Geier L. Z. Angew. Math. Mech. 66 (1986) 141
12. Rong H.W., Meng G., Wang X.D., Xu W., and Fang T. J. Sound Vibration 210 (1998) 483
13. Rong H., Xu W., and Fang T. J. Sound Vibration 283 (2005) 1250
14. Huang Z.L., Zhu W.Q., Ni Y.Q., and Ko J.M. J. Sound Vibration 254 (2002) 245
15. Xie W.C. J. Sound Vibration 289 (2006) 171
16. Nayfeh A.H. Perturbation Methods (1973), Wiley
17. Nayfeh A.H., and Mook D.T. Nonlinear Oscillations (1979), Wiley
18. Arnold L. Random Dynamical Systems (1998), Springer-Verlag, Berlin
19. Zillmer R., and Pikovsky A. Phys. Rev. E 67 (2003) 061117
20. Bourret R.C. Physica 54 (1971) 623
21. Bourret R.C., Frisch U., and Pouquet A. Physica 65 (1973) 303
22. Mallick K., and Marcq P. Eur. Phys. J. B 36 (2003) 119
23. Mallick K., and Marcq P. Eur. Phys. J. B 38 (2004) 99
24. Hansel D., and Luciani J.F. J. Stat. Phys. 54 (1989) 971
25. Tessieri L., and Izrailev F.M. Phys. Rev. E 62 (2000) 3090
26. Imkeller P., and Lederer C. Dyn. Stab. Syst. 14 (1999) 385
27. Mallick K., and Marcq P. Phys. Rev. E 66 (2002) 041113
28. Mallick K., and Marcq P. J. Stat. Phys 119 (2005) 1-33
29. Aumaître S., Pétrélis F., and Mallick K. Phys. Rev. Lett. 95 (2005) 064101
30. Hänggi P. In: Moss F., and McClintock P.V.E. (Eds). Noise in Dynamical Systems, vol. 1 (1989), Cambridge University Press, Cambridge
31. San Miguel M., and Sancho J.M. In: Moss F., and McClintock P.V.E. (Eds). Noise in Dynamical Systems, vol. 1 (1989), Cambridge University Press, Cambridge
32. Jung P., and Hänggi P. Phys. Rev. A 35 (1987) 4464
33. Hänggi P., and Jung P. Adv. Chem. Phys. 89 (1995) 239
34. Wihstutz V. In: Crauel H., and Gundlach M. (Eds). Stochastic Dynamics (1999), Springer-Verlag, New York
35. Lindenberg K., and West B.J. Physica A 119 (1983) 485
36. Lindenberg K., and West B.J. Physica A 128 (1984) 25
37. Hänggi P., Marchesoni F., and Grigolini P. Z. Phys. B 56 (1984) 333
38. Marchesoni F. Phys. Rev. A 36 (1987) 4050
39. Tsironis G.P., and Grigolini P. Phys. Rev. Lett. 61 (1988) 7
40. We remark that the BFPE can also be derived using the original operator formalism used in [31] but we preferred here to use a systematic approach in which the approximations are derived from the exact functional Eq. (31)
41. H'walisz L., Jung P., Hänggi P., Talkner P., and Schimansky-Geier L. Z. Phys. B 77 (1989) 471
42. Madureira A.J.R., Hänggi P., Buonomano V., and Rodrigues Jr. W.A. Phys. Rev. E 51 (1995) 3849
43. Castro F., Snchez A.D., and Wio H.S. Phys. Rev. Lett. 75 (1995) 1691
44. Castro F., Wio H.S., and Abramson G. Phys. Rev. E 52 (1995) 159
45. Bray A.J., and Mckane A.J. Phys. Rev. Lett. 62 (1989) 493
46. Dykman M.I. Phys. Rev. A 42 (1990) 2020
47. Dubkov A.A., Agudov N.V., and Spagnolo B. Phys. Rev. E 69 (2004) 061103
48. Schimansky-Geier L., and Herzel H. J. Stat. Phys. 70 (1993) 141
49. Bena I., Van den Broeck C., Kawai R., and Lindenberg K. Phys. Rev. E 66 (2002) 045603R
50. Bena I., Van den Broeck C., Kawai R., and Lindenberg K. Phys. Rev. E 68 (2003) 041111. cond-mat/0501499