Large fluctuations in multiattractor systems and the generalized kramers problem

Journal of Statistical Physics

Volumn 97, Issue 3-4, 1999, Pages 609-676

  Soskin, S M ^a  

^a INSTITUTE OF HYDROBIOLOGY   (Ukraine)

Author keywords

Action; Detailed balance; First passage problem; Kramers problem; Large fluctuation; Master equation; Most probable direct transition path; Multiattractor system; Probability flux; Saddle connection; Time reversed path; Variational problem

Indexed keywords

EID: 0033235602     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004663224988     Document Type: Article

References (60)

1. R. Landauer, in Noise in Nonlinear Dynamical Systems, F. Moss and P. V. E. McClintock, eds. (Cambridge University Press, Cambridge, 1989), Vol. 1, p. 1.
2. H. A. Kramers, Physica 7:284 (1940).
3. L. Pontryagin, A. Andronov, and A. Vitt, Zh. Eksp. Teor. Fiz. 3:165 (1933); see the English translation in Noise in Nonlinear Dynamical Systems, F. Moss and P. V. E. McClintock, eds. (Cambridge University Press, Cambridge, 1989), Vol. 1, p. 329.
4. L. Pontryagin, A. Andronov, and A. Vitt, Zh. Eksp. Teor. Fiz. 3:165 (1933); see the English translation in Noise in Nonlinear Dynamical Systems, F. Moss and P. V. E. McClintock, eds. (Cambridge University Press, Cambridge, 1989), Vol. 1, p. 329.
5. S. Arrhenius, Z. Phys. Chem (Leipzig) 4:226 (1889).
6. P. Hanggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62:251 (1990).
7. V. I. Mel'nikov, Phys. Rep. 209:1 (1991).
8. V. I. Mel'nikov, Sov. Phys. JETP 60:380 (1984).
9. V. Privman and H. L. Frisch, J. Chem. Phys. 94:8216 (1991).
10. V. A. Schneidman, Phys. Rev. E 56:5257 (1997).
11. S. M. Soskin et al., in Unsolved Problems of Noise, D. Abbot, ed. (American Institute of Physics, in press); S. M. Soskin, V. I. Sheka, T. L. Linnik et al., in Stochaos: Stochastic and Chaotic Dynamics in the Lakes, D. S. Broomhead. E. A. Luchinskaya, P. V. E. McClintock, and T. Mullin, eds. (American Institute of Physics, Woodbury, NY, in press).
12. S. M. Soskin et al., in Unsolved Problems of Noise, D. Abbot, ed. (American Institute of Physics, in press); S. M. Soskin, V. I. Sheka, T. L. Linnik et al., in Stochaos: Stochastic and Chaotic Dynamics in the Lakes, D. S. Broomhead. E. A. Luchinskaya, P. V. E. McClintock, and T. Mullin, eds. (American Institute of Physics, Woodbury, NY, in press).
13. M. I. Freidlin and A. D. Wentzell, Random Perturbations in Dynamical Systems (Springer-Verlag, New York, 1984).
14. L. Onsager and S. Muchlup, Phys. Rev. 91:1505 (1953): S. Muchlup and L. Onsager, Phys. Rev. 91:1512 (1953).
15. L. Onsager and S. Muchlup, Phys. Rev. 91:1505 (1953): S. Muchlup and L. Onsager, Phys. Rev. 91:1512 (1953).
16. R. P. Feinman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
17. A. D. Wentzell and M. I. Freidlin, Russ. Math. Surveys 25:1 (1970).
18. M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, Nuovo Cimento D 17:661 (1995).
19. A. R. Bulsara and L. Gamaitoni, Phys. Today (March 1996) 39.
20. M. Magnasco, Phys. Rev. Lett. 71:1477 (1993).
21. R. Astumian and M. Bier, Phys. Rev. Lett. 72:1766 (1994).
22. J. Prost, J. Chauwin, L. Peliti, and A. Adjari, Phys. Rev. Lett. 72:2652 (1994).
23. C. Doering, W. Horsthemke, and J. Riordan, Phys. Rev. Lett. 72:2984 (1994).
24. D. R. Chialvo and M. M. Millonas, Phys. Lett. A 209:21 (1995).
25. M. I. Dykman, H. Rabitz, V. N. Smelyanskiy, and B. E. Vugmeister, Phys. Rev. Lett. 79:1178 (1997).
26. V. N. Smelyanskiy and M. I. Dykman, Phys. Rev. E 55:2516 (1997).
27. B. E. Vugmeister and H. Rabitz, Phys. Rev. E 55:2522 (1997).
28. B. J. Matkowsky and Z. Schuss, SIAM J. Appl. Math. 33:365 (1977).
29. R. Graham and T. Tel, Phys. Rev. A 33:1322 (1986).
30. P. Talkner, Z. Phys. B 68:201 (1987).
31. R. S. Maier and D. L. Stein, Phys. Rev. Lett. 71:1783 (1993).
32. R. S. Maier and D. L. Stein, J. Stat. Phys. 83:291 (1996).
33. M. I. Dykman and M. A. Krivoglaz, Sov. Phys. JETP 50:30 (1979).
34. R. L. Kautz, Phys. Rev. A 38:2066 (1988).
35. A. J. McKane, A. J. Bray, and H. C. Luckock, Phys. Rev. A 41:644 (1990).
36. M. I. Dykman, Phys. Rev. A 42:2020 (1990).
37. M. I. Dykman, P. V. E. McClintock. V. N. Smelyanski, N. D. Stein, and N. G. Stocks, Phys. Rev. Lett. 68:4547 (1992).
38. N. G. van Kampen, Stochastic Processes in Physics and Chemistry, 6th ed. (North-Holland, Amsterdam, 1990).
39. H. Risken, The Fokker-Planck Equation, 2nd ed. (Springer-Verlag, Berlin, 1992).
40. L. E. Elsgolc, Calcalus of Variations (Pergamon Press, London, 1961).
41. L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon, London, 1976).
42. R. Graham, D. Roekaerts, and T. Tel. Phys. Rev. A 31:3364 (1985).
43. R. Barone and G. Paterno, Physics and Applications of the Josephson Effect (Wiley, New York, 1982).
44. A. D. Hibbs, A. L. Singsaas, E. W. Jacobs, A. R. Bulsara, J. J. Bekkedahl, and F. Moss. J. Appl. Phys. 77:2582 (1995).
45. I. Kh. Kaulman, D. G. Luchinsky, P. V. E. McClintock, S. M. Soskin, and N. D. Stein, Phys. Rev. E 57:78 (1998).
46. M. I. Dykman, M. M. Millonas, and V. N. Smelyanskiy, Phys. Lett. A 195:53 (1994).
47. M. I. Dykman, E. Mori, J. Ross, and P. M. Hunt, J. Chem. Phys. 100:5735 (1994).
48. N. N. Bogolyubov and Yu. A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillators (Gordon and Breach, New York, 1961).
49. S. M. Soskin, Physica A 155:401 (1989).
50. V. I. Mel'nikov, Sov. Phys. JETP 61:855 (1985).
51. S. M. Soskin, Phys. Rev. E 50:R44 (1994).
52. D. G. Luchinsky, P. V. E. McClintock, S. M. Soskin, and R. Mannella, Phys. Rev. Lett. 76:4453 (1996).
53. R. Mannella, S. M. Soskin, and P. V. E. McClintock, Global bifurcations in periodically driven zero-dispersion systems and problem of large fluctuations, unpublished.
54. B. E. Vugmeister, J. Botina, and H. Rabitz, Phys. Rev. E 55:5338 (1997).
55. O. M. Yevtushenko and K. Richter, Phys. Rev. B 57:14839 (1998).
56. E. Ben-Jacob, D. J. Bergman, B. J. Matkowsky, and Z. Schuss, Phys. Rev. A 26:2805 (1982).
57. H. D. Vollmer and H. Risken, Z. Phys. B 52:159 (1983).
58. P. Jung and H. Risken, Z. Phys. B 54:357 (1984).
59. B. Hille, Ionic Channels of Excitable Membranes (Sinauer Associates Inc.. Sunderland, 1992).
60. R. S. Eisenberg, J. Membrane Biol. 150:1 (1996).