Stochastic multiplicative processes with reset events

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

Volumn 59, Issue 5, 1999, Pages 4945-4948

  Manrubia, Susanna C ^a   Zanette, Damián H ^b  

^a FRITZ HABER INSTITUT DER MAX PLANCK GESELLSCHAFT   (Germany)

^b CENTRO ATÓMICO BARILOCHE   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000539930     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.4945     Document Type: Article

References (29)

1. J.-F. Gouyet, Physics and Fractal Structures (Masson and Springer, Paris, 1996).
2. J. J. Sepkowski, Jr., Paleobiology 19, 43 (1991)
3. D. M. Raup, Extinction: Bad genes or bad luck? (Oxford University Press, Oxford, 1993)
4. K. Sneppen, P. Bak, H. Flyvbjerg, and M. H. Jensen, Proc. Natl. Acad. Sci. USA 92, 5209 (1995)
5. R. V. Solé, S. C. Manrubia, M. J. Benton, and P. Bak, Nature (London) 388, 764 (1997).
6. G. K. Zipf, Human Behavior and the Principle of Least Effort (Addison-Wesley, Cambridge, MA, 1949)
7. H. A. Makse, S. Havlin, and H. E. Stanley, Nature (London) 377, 608 (1995)
8. D. H. Zanette and S. C. Manrubia, Phys. Rev. Lett. 79, 523 (1997).
9. M. Schroeder, Fractal, Chaos, Power Laws (Freeman, New York, 1991).
10. J. P. Bouchaud, in Lévy Flights and Related Topics in Physics (Springer, Heidelberg, 1995)
11. J. Laherrère and D. Sornette, Eur. Phys. J. B 2, 525 (1998).
12. C. Tsallis, J. Stat. Phys. 52, 479 (1988)
13. E. M. F. Curado and C. Tsallis, J. Phys. A 24, L69 (1991).
14. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)
15. M. Paczuski, S. Maslov, and P. Bak, Phys. Rev. E 53, 414 (1996).
16. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992).
17. D. H. Zanette, Phys. Rev. E 49, 2779 (1994)
18. Phys. Rev. ES. C. Manrubia and D. H. Zanette 58, 295 (1998).
19. G. Grinstein, M. A. Muñoz, and Y. Tu, Phys. Rev. Lett. 76, 4376 (1996)
20. Phys. Rev. Lett.H. Takayasu, A.-H. Sato, and M. Takayasu, 79, 966 (1997)
21. D. Sornette, Phys. Rev. E 57, 4811 (1998).
22. M. Levy and S. Solomon, Int. J. Mod. Phys. C 7, 745 (1996)
23. D. Sornette and R. Cont, J. Phys. I 7, 431 (1997).
24. A. S. Mikhailov, Physica A 188, 367 (1992)
25. D. H. Zanette and A. S. Mikhailov, Phys. Rev. E 50, 1638 (1994).
26. The general form of the equation to be satisfied by the exponent α is (Formula presented) with (Formula presented) Considering the special case (Formula presented) is sufficient to reproduce the value of α obtained in Eq. (5). Complex values of this exponent lead to “log-periodic” distributions. For details, see D. Sornette, Phys. Rep. 297, 239 (1998)
27. P. Jögi, D. Sornette, and M. Blank, Phys. Rev. E 57, 120 (1998).
28. C. Sire, S. Majumdar, and A. Rudinger, Phys. Rev. E (to be published)
29. C. SireS. MajumdarA. Rudingere-print cond-mat/9810136, and references therein.