Characterizing the dynamics of stochastic bistable systems by measures of complexity

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

Volumn 55, Issue 5, 1997, Pages 5050-5059

  Witt, Annette ^a   Neiman, Alexander ^a   Kurths, Jürgen ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000345756     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.5050     Document Type: Article

References (50)

1. H A. Kramers, Physica7, 284 (1940).
2. P. Hänggi, P. Talkner and M. Berkovec, Rev. Mod. Phys62, 251 (1990);
3. V.I. Mel'nikov, Phys. Rep.209, 1 (1991);
4. Activated Barrier Crossing. Applications in Physics, Chemistry and Biology, edited by G.R. Fleming and P. Hänggi (World Scientific, Singapore, 1993).
5. F. Moss, in Some Problems in Statistical Physics, edited by G.H. Weiss (SIAM, Philadelphia, 1992);
6. in Stochastic Resonance in Physics and Biology, edited by F. Moss, A. Bulsara, and M. Shlesinger, special issue of J. Stat. Phys. 70 (1993);
7. F. Moss, D. Pierson and D. O'Gorman, Int. J. Bifurcat. and Chaos4, 1383 (1994);
8. K. Wiesenfeld and F. Moss, Nature373, 33 (1995);
9. Proceedings of the Second International Workshop on Stochastic Resonance, edited by R. Manella and P.V.E. McClintock [Nuovo Cimento D 17 (1995)].
10. J E. Levin and J P. Miller, Nature380, 165 (1996);
11. A. Bulsara and T. Zader, Phys. Rev. E54, 2185 (1996).
12. A. Neiman, B. Shulgin, V. Anishchenko, W. Ebeling, L. Schimansky-Geier and J. Freund, Phys. Rev. Lett76, 4299 (1996).
13. C R. Doering and J C. Gadoua, Phys. Rev. Lett.69, 2318 (1992);
14. U. Zuercher and C R. Doering, Phys. Rev. E47, 3862 (1993);
15. C. Van den Broeck, Phys. Rev. Eibid. 47, 3862 (1993);
16. M. Bier and R D. Astumian, Phys. Rev. Lett.71, 1649 (1993);
17. P. Hänggi, Phys. Lett.78A, 304 (1980);
18. P. Hänggi, Chem. Phys.180, 157 (1994);
19. P. Reimann, Phys. Rev. E49, 4938 (1994);
20. J J. Brey and J. Casado-Pascual, Phys. Rev. Eibid. 50, 116 (1994).
21. L. Pontryagin, A. Andronov, and A. Vitt, in Noise in Nonlinear Dynamical Systems, edited by F. Moss and P.V.E. McClintock (Cambridge University Press, Cambridge, 1989), Vol. 1, p. 329.
22. C W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1985).
23. C. Meunier and A D. Verga, J. Stat. Phys.50, 345 (1988);
24. R. Graham, in Noise in Nonlinear Dynamical Systems (Ref. [7]), p. 225.
25. S. Leibler, Nature370, 412 (1994).
26. P. Jung and P. Hänggi, Phys. Rev. A35, 4464 (1987);
27. E. Peacock-Lopez, F.J. de la Rubia, B J. West and K. Lindenberg, Phys. Lett. A136, 96 (1989).
28. P. Pechukas and P. Hänggi, Phys. Rev. Lett.73, 2772 (1994);
29. A.J.R. Madureira, P. Hänggi, V. Buonomano and W A. Rodrigues, Phys. Rev. E51, 3849 (1995).
30. F. Marchesoni, L. Gammaitoni, E. Menichella-Saetta and S. Santucci, Phys. Lett. A201, 275 (1995).
31. Lyapunov Exponents, edited by L. Arnold and V. Wihstutz, Lecture Notes in Mathematics Vol. 1186 (Springer-Verlag, Berlin, 1984); ibid., Lecture Notes in Mathematics Vol. 1486 (Springer-Verlag, Berlin, 1991).
32. W. Ebeling, H. Herzel, W. Richert and L. Schimansky-Geier, Z. Angew. Math. Mech.66, 141 (1986);
33. L. Schimansky-Geier and H. Herzel, J. Stat. Phys70, 141 (1993).
34. P. Jung, Phys. Rep.234, 175 (1993).
35. Handbook of Mathematical Functions, Natl. Bur. Stand. Appl. Math. Ser. No. 55, edited by M. Abramowitz and I. Stegun (U.S. GPO, Washington, DC, 1964).
36. M C. Mackey, A. Longtin and A. Lasota, J. Stat. Phys.60, 735 (1990).
37. R. Wackerbauer, A. Witt, H. Atmanspacher, J. Kurths and H. Scheingraber, Chaos, Solitons Fractals4, 133 (1994).
38. A. Witt, J. Kurths, F. Krause and K. Fischer, Geophys. Astrophys. Fluid Dyn.77, 79 (1995).
39. J. Kurths, A. Voss, A. Witt, P. Saparin, H J. Kleiner and N. Wessel, CHAOS5, 88 (1995).
40. B.-L. Hao, Physica D51, 611 (1991).
41. C E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Urbana, 1949).
42. P. Grassberger, Int. J. Theor. Phys.25, 907 (1986);
43. P. Grassberger, Physica A140, 319 (1986).
44. H. Haken, Information and Self-Organisation (Springer, Berlin, 1988).
45. J E. Hopcroft and J D. Ullman, Introduction to Automata Theory (Addison-Wesley, Reading, MA, 1979).
46. J P. Crutchfield and K. Young, Phys. Rev. Lett.63, 105 (1989);
47. in Complexity, Entropy, and the Physics of Information, edited by W. Zurek (Addison-Wesley, Reading, MA, 1989), pp. 223–269;
48. J.P. Crutchfield, in Measures of Complexity and Chaos, edited by N. Abraham (Plenum New York, 1989), pp. 327–338.
49. B. Shulgin, A. Neiman and V. Anishchenko, Phys. Rev. Lett.75, 4157 (1995).
50. L. Schimansky-Geier, J. Freund, A. Neiman, and B. Shulgin (unpublished).