Solution of the boundary value problem for optimal escape in continuous stochastic systems and maps

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 72, Issue 3, 2005, Pages

  Beri, S ^a   Mannella, R ^a,b   Luchinsky, D G ^a   Silchenko, A N ^a   McClintock, P V E ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICAL SYSTEMS; OPTIMAL ESCAPE PATH; OPTIMAL TRAJECTORIES; PARAMETERS CHARACTERIZING;

ACTIVATION ENERGY; MAPS; OPTIMAL CONTROL SYSTEMS; STOCHASTIC CONTROL SYSTEMS; TOPOLOGY; TRAJECTORIES;

BOUNDARY VALUE PROBLEMS;

EID: 28844446321     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.036131     Document Type: Article

References (52)

1. M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, Nuovo Cimento D NIFDAV 0392-6737 17, 661 (1995).
2. F. Jülicher, F. Ajdari, and J. Prost, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.69.1269 69, 1269 (1997).
3. M. O. Magnasco, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.1477 71, 1477 (1993).
4. M. I. Dykman, H. Rabitz, V. N. Smelyanskiy, and B. E. Vugmeister, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.1178 79, 1178 (1997).
5. V. N. Smelyanskiy, M. I. Dykman, H. Rabitz, B. E. Vugmeister, S. L. Bernasek, and A. B. Bocarsly, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.479090 110, 11488 (1999).
6. M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.4337 84, 4337 (2000).
7. M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.4105 60, 4105 (1999).
8. M. P. van Exter, R. F. M. Hendriks, and J. P. Woerdman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.2080 57, 2080 (1998).
9. M. P. van Exter, M. B. Willemsen, and J. P. Woerdman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.4191 58, 4191 (1998).
10. V. A. Gaisyonok, E. V. Grigorieva, and S. A. Kashchenko, Opt. Commun. OPCOB8 0030-4018 10.1016/0030-4018(95)00587-0 124, 408 (1996).
11. V. N. Chizhevsky, E. V. Grigorieva, and S. A. Kashchenko, Opt. Commun. OPCOB8 0030-4018 10.1016/S0030-4018(96)00458-0 133, 189 (1997).
12. R. S. Eisenberg, M. M. Klosek, and Z. Schuss, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.468704 102, 1767 (1995).
13. R. S. Maier and D. L. Stein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.1358 85, 1358 (2000).
14. R. S. Maier and D. L. Stein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.1783 71, 1783 (1993).
15. R. S. Maier and D. L. Stein, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF02183736 83, 291 (1996).
16. R. S. Maier and D. L. Stein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.4860 77, 4860 (1996).
17. V. N. Smelyanskiy and M. I. Dykman, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.2516 55, 2516 (1997).
18. V. N. Smelyanskiy, M. I. Dykman, and R. S. Maier, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.2369 55, 2369 (1997).
19. M. I. Dykman, M. M. Millonas, and V. N. Smelyanskiy, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(94)90426-X 195, 53 (1994).
20. V. N. Smelyanskiy, M. I. Dykman, and B. Golding, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.3193 82, 3193 (1999).
21. R. S. Maier and D. L. Stein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3942 86, 3942 (2001).
22. J. Lehmann, P. Reimann, and P. Hänggi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.1639 84, 1639 (2000).
23. J. Lehmann, P. Reimann, and P. Hänggi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.6282 62, 6282 (2000).
24. A. Hamm and R. Graham, J. Stat. Phys. JSTPBS 0022-4715 66, 6891 (1992).
25. R. Graham and T. Tel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.52.9 52, 9 (1984).
26. R. Graham and T. Tel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.31.1109 31, 1109 (1985).
27. R. Graham, in Noise in Nonlinear Dynamical Systems, edited by, F. Moss, and, P. V. E. McClintock, (Cambridge University Press, Cambridge, U.K., 1989), vol. 1, pp. 225-278.
28. H. R. Jauslin, Physica A PHYADX 0378-4371 10.1016/0378-4371(87)90151-8 144, 179 (1987).
29. M. V. Day, Stochastics STOCB2 0090-9491 20, 121 (1987).
30. P. Talkner, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01304226 68, 201 (1987).
31. R. S. Maier and D. L. Stein, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139994271753 57, 752 (1997).
32. M. I. Dykman, D. G. Luchinsky, P. V. E. McClintock, and V. N. Smelyanskiy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.5229 77, 5229 (1996).
33. V. N. Smelyanskiy, M. I. Dykman, H. Rabitz, and B. E. Vugmeister, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.3113 79, 3113 (1997).
34. T. Naeh, B. Kłosek, M. M. Matkovsky, and Z. Schuss, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0150036 50, 595 (1990).
35. M. I. Dykman, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 8, 747 (1998).
36. D. G. Luchinsky, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127402004528 12, 583 (2002).
37. A. N. Silchenko, S. Beri, D. G. Luchinsky, and P. V. E. McClintock, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.174104 91, 174104 (2003).
38. A. Silchenko, S. Beri, D. G. Luchinsky, and P. V. E. McClintock, Appl. Nonlinear Dyn. (Saratov) 11, 38 (2003).
39. S. Kraut and U. Feudel, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.015204 67, 015204 (R) (2003).
40. P. D. Beale, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.3998 40, 3998 (1989).
41. D. Ludwig, SIAM Rev. SIREAD 0036-1445 10.1137/1017070 17, 605 (1975).
42. D. G. Luchinsky, P. V. E. McClintock, and M. I. Dykman, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/61/8/001 61, 889 (1998).
43. M. I. Dykman P. V. E. McClintock, V. N. Smelyanski, N. D. Stein, and N. G. Stocks, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.2718 68, 2718 (1992).
44. M. Freidlin and A. D. Wentzel, Random Perturbations in Dynamical Systems (Springer, New York, 1984).
45. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, Berlin, 1978).
46. Some authors use for such a point the term focus. See for instance A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, Qualitative Theory of Second-Order Dynamical Systems (Wiley, New York, 1973).
47. B. van der Pol, Philos. Mag. PHMAA4 0031-8086 6, 763 (1928).
48. M. Henon, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01608556 50, 69 (1976).
49. E. Ott, Chaos in Dynamical System (Cambridge University Press, Cambridge, U.K., 2002).
50. P. Grassberger, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/22/16/018 22, 3283 (1989).
51. S. W. McDonald, C. Grebogi, E. Ott, and J. A. Yorke, Physica D PDNPDT 0167-2789 10.1016/0167-2789(85)90001-6 17, 125 (1985).
52. G. Julia, J. Math. Pures Appl. JMPAAM 0021-7824 8, 47 (1918).