Concept of complexity in random dynamical systems

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

Volumn 53, Issue 3, 1996, Pages 2087-2098

  Loreto, Vittorio ^a,b   Paladin, Giovanni ^a,b   Vulpiani, Angelo ^a,b  

^a UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000816581     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.53.2087     Document Type: Article

References (50)

1. F. Moss, P. W. E. McClintock, Noise in Nonlinear Dynamical Systems (Cambridge University Press, Cambridge, 1989), Vols. 1 3.
2. J. P. Crutchfield, D. J. Farmer and B. A. Huberman, Phys. Rep.92, 45 (1982).
3. H. Herzel, W. Ebeling and Th. Schulmeister, Z. Naturforsch. A41, 801 (1986).
4. H. Herzel and B. Pompe, Phys. Lett. A122, 121 (1987).
5. A. R. Bulsara, E. W. Jacobs and W. C. Schieve, Phys. Rev. A42, 4614 (1990).
6. Z. Y. Chen, Phys. Rev. A42, 5837 (1990).
7. K. Matsumoto and I. Tsuda, J. Stat. Phys.31, 87 (1983).
8. R. J. Deissler and D. J. Farmer, Physica D55, 155 (1992).
9. R. Benzi, A. Sutera and A. Vulpiani, J. Phys. A14, L453 (1981).
10. R. Benzi, G. Parisi, A. Sutera and A. Vulpiani, Tellus 34, 10 (1982).
11. C. Nicolis, Tellus 34, 1 (1982).
12. For a general review on stochastic resonance see J. Stat. Phys. 70, No. 1/2 (1993).
13. A. Wolf, J. B. Swift, H. L. Swinney and J. A. Vastano, Physica D16, 285 (1985).
14. C. E. Shannon and W. Weaver, The Mathematical Theory of Communications (University of Illinois Press, Urbana, 1949).
15. E. Aurell, G. Boffetta, A. Crisanti, G. Paladin and A. Vulpiani, Phys. Rev. E53, 2337 (1996).
16. G. Lacorata and G. Paladin, J. Phys. A26, 3463 (1993).
17. P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. A38, 364 (1988).
18. P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).
19. N. Platt, E. A. Spiegel and C. Tresser, Phys. Rev. Lett.70, 279 (1993);
20. J. F. Heagy, N. Platt and S. M. Hammel, Phys. Rev. E49, 1140 (1994).
21. C. van der Broeck and G. Nicolis, Phys. Rev. E48, 4845 (1993).
22. F. Martinelli and E. Scoppola, Commun. Math. Phys.120, 25 (1988).
23. E. D. Lorenz, J. Atmos. Sci.20, 130 (1963).
24. A. Crisanti, M. Falcioni, G. Paladin and A. Vulpiani, J. Phys. 27A, L597 (1994).
25. G. Paladin, M. Serva and A. Vulpiani, Phys. Rev. Lett. 74, 66 (1995).
26. J. S. Nicolis, G. Mayer Kress and G. Haubs, Z. Naturforsch. Teil A38, 1157 (1983);
27. B. Pompe, J. Kruscha and R. W. Leven, Z. Naturforsch. Teil A41, 801 (1986);
28. J. S. Nicolis, Dynamics of Hierarchical Systems: An Evolutionary Approach (Springer Verlag, Berlin, 1986);
29. R. Feistel and W. Eberling, Evolution of Complex Systems: Self Organization, Entropy and Development (Kluwer Academic Press, Dordrecht, 1989).
30. G. Paladin and A. Vulpiani, Phys. Rep. 156, 147 (1987).
31. For a physical discussion see J. Ford, Phys. Today 36, (4), 40 (1983).
32. A. Crisanti, M. Falcioni, G. Paladin and A. Vulpiani, Riv. Nuovo Cimento 14, 1 (1991).
33. J. P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985).
34. C. Van Der Broeck and T. Tel, in From Phase Transitions to Chaos: Topics in Modern Statistical Physics, edited by G. Gyorgyi, I. Kondor, L. Sasvari, and T. Tel (World Scientific, Singapore, 1992), p. 227.
35. R. Kapral and S. J. Fraser, J. Stat. Phys. 70, 61 (1993).
36. L. Yu, E. Ott and Q. Chen, Phys. Rev. Lett.65, 2935 (1990);
37. L. Yu, E. Ott and Q. Chen, Physica D53, 102 (1993)
38. S. Galluccio and A. Vulpiani, Physica A212, 75 (1994).
39. J. Huang and D. L. Turcotte, Geophys. Res. Lett. 17, 223 (1990);
40. J. Huang and D. L. Turcotte, Nature 348, 234 (1990)
41. R. Burridge and L. Knopoff, Bull. Seismol. Soc. Am. 57, 341 (1967).
42. G. Narkounskaia, J. Huang and D. L. Turcotte, J. Stat. Phys. 68, 1151 (1992).
43. T. A. Witten and L. M. Sander, Phys. Rev. Lett. 47, 1400 (1981).
44. L. Pietronero and H. J. Wiesmann, J. Stat. Phys.36, 811 (1984).
45. P. Bak and K. Sneppen, Phys. Rev. Lett. 71, 4083 (1993).
46. D. Wikinson and J. F. Willemsen, Physica A16, 3365 (1983).
47. Y. C. Zhang, Phys. Rev. Lett. 63, 470 (1987).
48. E. Caglioti and V. Loreto (unpublished).
49. K. Chen, P. Bak and M. H. Jensen, Phys. Lett. A149, 207 (1990).
50. E. Caglioti and V. Loreto, Phys. Rev. E 53 (to be published).