Random maps and attractors in random Boolean networks

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

Volumn 72, Issue 4, 2005, Pages

  Samuelsson, Björn ^a   Troein, Carl ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; GRAPH THEORY; REAL TIME SYSTEMS; TOPOLOGY;

ASYMPTOTIC EXPANSIONS; BOOLEAN NETWORKS; CUMULANTS; RANDOM MAPS;

BOOLEAN ALGEBRA;

EID: 33244476083     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.046112     Document Type: Article

References (34)

1. S. A. Kauffman, J. Theor. Biol. JTBIAP 0022-5193 10.1016/0022-5193(69) 90015-0 22, 437 (1969).
2. M. Aldana-Gonzalez, S. Coppersmith, and L. P. Kadanoff, in Perspectives and Problems in Nonlinear Science, edited by, E. Kaplan, J. E. Marsden, and, K. R. Sreenivasan, (Springer, 2003), p. 23.
3. J. E. S. Socolar and S. A. Kauffman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.068702 90, 068702 (2003).
4. B. Derrida and Y. Pomeau, Europhys. Lett. EULEEJ 0295-5075 1, 45 (1986).
5. U. Bastolla and G. Parisi, Physica D PDNPDT 0167-2789 115, 203 (1998).
6. U. Bastolla and G. Parisi, J. Theor. Biol. JTBIAP 0022-5193 10.1006/jtbi.1997.0423 187, 117 (1997).
7. H. Flyvbjerg, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/21/19/006 21, L955 (1988).
8. U. Bastolla and G. Parisi, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97)00242-X 115, 219 (1998).
9. S. Kauffman, C. Peterson, B. Samuelsson, and C. Troein, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0407783101 101, 17102 (2004).
10. B. Drossel, T. Mihaljev, and F. Greil, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.088701 94, 088701 (2005).
11. H. Flyvbjerg and H. J. Kjær, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/21/7/031 21, 1695 (1988).
12. B. Derrida and H. Flyvbjerg, J. Phys. (Paris) JOPQAG 0302-0738 48, 971 (1987).
13. B. Samuelsson and C. Troein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.098701 90, 098701 (2003).
14. V. Kaufman and B. Drossel, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2005-00034-6 43, 115 (2004).
15. S. Bilke and F. Sjunnesson, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.016129 65, 016129 (2001).
16. S. Kauffman, C. Peterson, B. Samuelsson, and C. Troein, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.2036429100 100, 14796 (2003).
17. K. Klemm and S. Bornholdt, cond-mat/0411102 (2004).
18. M. D. Kruskal, Am. Math. Monthly AMMYAE 61, 392 (1954).
19. B. Harris, Ann. Math. Stat. AASTAD 0003-4851 31, 1045 (1960).
20. S. M. Ross, J. Appl. Probab. JPRBAM 0021-9002 18, 309 (1981).
21. J. Kupka, J. Appl. Probab. JPRBAM 0021-9002 27, 202 (1990).
22. L. Katz, Ann. Math. Stat. AASTAD 0003-4851 26, 512 (1955).
23. J. Jaworski, J. Appl. Probab. JPRBAM 0021-9002 21, 186 (1984).
24. P. J. Donnelly, W. J. Ewens, and S. Padmadisastra, Adv. Appl. Probab. AAPBBD 0001-8678 23, 437 (1991).
25. B. J. English, J. Appl. Probab. JPRBAM 0021-9002 30, 167 (1993).
26. J. C. Hansen and J. Jaworski, J. Appl. Probab. JPRBAM 0021-9002 39, 712 (2002).
27. B. Bollabás, in Random Graphs (Academic Press, London, 1985).
28. V. E. Stepanov, Theor. Probab. Appl. TPRBAU 0040-585X 14, 612 (1969).
29. D. Romero and F. Zertuche, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/13/304 36, 3691 (2003).
30. H.-K. Hwang, Adv. Appl. Probab. AAPBBD 0001-8678 10.1239/aap/1029955143 31, 448 (1999).
31. W. Feller, in An Introduction to Probability Theory and Its Applications, Vol. 1 (Wiley, New York, 1968).
32. G. B. Arfken and H. J. Weber, in Mathematical Methods for Physicists, 5th ed. (Harcourt/Academic Press, 2001).
33. I. S. Gradshteyn and I. M. Ryzhik, in Table of Integrals, Series, and Products (Academic Press, London, 1965).
34. C. Berge, in Principles of Combinatorics (Academic Press, New York, 1971).