Attractor and basin entropies of random Boolean networks under asynchronous stochastic update

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

Volumn 82, Issue 3, 2010, Pages

  Shreim, Amer ^a   Berdahl, Andrew ^a,b   Greil, Florian ^c   Davidsen, Jörn ^a   Paczuski, Maya ^a  

^a UNIVERSITY OF CALGARY   (Canada)

^b PRINCETON UNIVERSITY   (United States)

^c DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

OCCUPATION PROBABILITY; RANDOM BOOLEAN NETWORKS; STATE SPACE; STEADY STATE; SYSTEM SIZE;

ENTROPY; STOCHASTIC SYSTEMS;

DYNAMICAL SYSTEMS;

EID: 77957281163     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.035102     Document Type: Article

References (28)

1. M. Lagomarsino, B. Bassetti, G. Castellani, and D. Remondini, Mol. BioSys. 5, 335 (2009). 10.1039/b816841p
2. M. Aldana, S. Coppersmith, and L. Kadanoff, in Perspectives and Problems in Nonlinear Science, edited by, E. Kaplan, J. Marsden, and, K. Sreenivasan, (Springer, New York, 2003), pp. 23-89.
3. S. Bornholdt, J. R. Soc., Interface 5, S85 (2008). 10.1098/rsif.2008. 0132.focus
4. R. Albert, J. Cell. Sci. 118, 4947 (2005). 10.1242/jcs.02714
5. F. Li, T. Long, Y. Lu, Q. Ouyang, and C. Tang, Proc. Natl. Acad. Sci. U.S.A. 101, 4781 (2004). 10.1073/pnas.0305937101
6. M. Rosen-Zvi, A. Engel, and I. Kanter, Phys. Rev. Lett. 87, 078101 (2001). 10.1103/PhysRevLett.87.078101
7. M. Paczuski, K. E. Bassler, and Á. Corral, Phys. Rev. Lett. 84, 3185 (2000). 10.1103/PhysRevLett.84.3185
8. S. Kauffman, J. Theor. Biol. 22, 437 (1969). 10.1016/0022-5193(69)90015-0
9. B. Drossel, in Reviews of Nonlinear Dynamics and Complexity, edited by, H. Schuster, (Wiley-VCH, Weinheim, 2008), Vol. 1.
10. B. Derrida and Y. Pomeau, EPL 1, 45 (1986). 10.1209/0295-5075/1/2/001
11. B. Drossel, Phys. Rev. E 72, 016110 (2005). 10.1103/PhysRevE.72.016110
12. B. Drossel, T. Mihaljev, and F. Greil, Phys. Rev. Lett. 94, 088701 (2005). 10.1103/PhysRevLett.94.088701
13. B. Samuelsson and C. Troein, Phys. Rev. Lett. 90, 098701 (2003). 10.1103/PhysRevLett.90.098701
14. U. Bastolla and G. Parisi, Physica D 98, 1 (1996). 10.1016/0167-2789(96) 00060-7
15. A. Berdahl, A. Shreim, V. Sood, M. Paczuski, and J. Davidsen, New J. Phys. 11, 043024 (2009). 10.1088/1367-2630/11/4/043024
16. A. Bhattacharjya and S. Liang, Phys. Rev. Lett. 77, 1644 (1996). 10.1103/PhysRevLett.77.1644
17. P. Krawitz and I. Shmulevich, Phys. Rev. Lett. 98, 158701 (2007). 10.1103/PhysRevLett.98.158701
18. B. A. Huberman and N. S. Glance, Proc. Natl. Acad. Sci. U.S.A. 90, 7716 (1993). 10.1073/pnas.90.16.7716
19. I. Harvey and T. Bossomaier, Proceedings of the Fourth European Conference on Artificial Life (MIT Press, Cambridge, 1997), pp. 67-75.
20. K. Klemm and S. Bornholdt, Phys. Rev. E 72, 055101 (R) (2005). 10.1103/PhysRevE.72.055101
21. L. Glass and C. Hill, EPL 41, 599 (1998). 10.1209/epl/i1998-00199-0
22. F. Greil and B. Drossel, Phys. Rev. Lett. 95, 048701 (2005). 10.1103/PhysRevLett.95.048701
23. M. I. Davidich and S. Bornholdt, PLoS ONE 3, e1672 (2008). 10.1371/journal.pone.0001672
24. S. Braunewell and S. Bornholdt, J. Theor. Biol. 245, 638 (2007). 10.1016/j.jtbi.2006.11.012
25. H. Flyvbjerg and N. Kjaer, J. Phys. A 21, 1695 (1988). 10.1088/0305-4470/21/7/031
26. - 6 / N.
27. To check for consistency, we tested whether there were states identified erroneously as transient that could be reached from an attractor. This was never observed.
28. Note that the corresponding distribution for CRBNs, P a (l) in the notation of Ref., is broad for all K2, exactly the opposite as found here for ARBNs.