Boolean dynamics of networks with scale-free topology

Physica D: Nonlinear Phenomena

Volumn 185, Issue 1, 2003, Pages 45-66

  Aldana, Maximino ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

Boolean networks; Dynamical phase transition; Evolvability; Scale free topology; Stability

Indexed keywords

NUMERICAL METHODS; PHASE TRANSITIONS; PROBABILITY; TOPOLOGY; WORLD WIDE WEB;

BOOLEAN NETWORKS;

BOOLEAN ALGEBRA;

EID: 0141903547     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(03)00174-X     Document Type: Article

References (27)

1. Albert R., Barabási A.-L., Statistical mechanics of complex networks. Rev. Modern Phys. 74(1):2002;47-97.
2. Albert R., Jeong H., Barabási A.-L., Diameter of the world-wide web. Nature. 401:1999;130-131.
3. Albert R., Jeong H., Barabási A.-L., Error and attack tolerance of complex networks. Nature. 406:1999;378-381.
4. B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, J.D. Watson, Molecular Biology of the Cell, Garland, New York, 1994.
5. M. Aldana-González, S. Copersmith, L.P. Kadanoff, Boolean dynamics with random couplings, Springer Appl. Math. Sci. Ser., in press. http://arXiv.org/pdf/nlin.AO/0204062.
6. A.-L. Barabási, Linked: The New Science of Networks, Perseus Publishing, Cambridge, MA, 2002.
7. Bilke S., Sjunnesson F., Stability of the Kauffman model. Phys. Rev. E. 65:2001;16129.
8. Camacho J., Guimerá R., Nunes Amaral L.A., Robust patterns in food web structure. Phys. Rev. Lett. 88(22):2002;228102.
9. Derrida B., Flyvbjerg H., The random map model: a disordered model with deterministic dynamics. J. Phys. 48:1987;971-978.
10. Derrida B., Pomeau Y., Random networks of automata: a simple annealed approximation. Europhys. Lett. 1(2):1986;45-49.
11. Flyvbjerg H., Kjaer N.J., Exact solution of the Kauffman model with connectivity one. J. Phys. A. 21(7):1988;1695-1718.
12. Fox J.J., Hill C.C., From topology to dynamics in biochemical networks. Chaos. 11(4):2001;809-815.
13. Huang S., Ingber D.E., Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks. Exp. Cell Res. 261(1):2000;91-103.
14. Jeong H., Tombor B., Albert R., Oltvai Z.N., Barabási A.-L., The large-scale organization of metabolic networks. Nature. 407:2000;651-654.
15. Jeong H., Mason S., Barabási A.-L., Oltvai Z.N., Lethality and centrality in protein networks. Nature. 411:2001;41.
16. Kauffman S.A., Metabolic stability and epigenesis in randomly constructed nets. J. Theor. Biol. 22:1969;437-467.
17. Kauffman S.A., Requirements for evolvability in complex systems: orderly dynamics and frozen components. Physica D. 42(1-3):1990;135-152.
18. S.A. Kauffman, The Origins of Order: Self-organization and Selection in Evolution, Oxford University Press, Oxford, 1993.
19. Luque B., Solé R.V., Phase transitions in random networks: simple analytic determination of critical points. Phys. Rev. E. 55(1):1997;257-260.
20. Maslov S., Sneppen K., Specificity and stability in topology of protein networks. Science. 296:2002;910-913.
21. Newman M.E.J., The structure of scientific collaboration networks. Proc. Natl. Acad. Sci. 98(2):2001;404-409.
22. Oosawa C., Savageau M.A., Effects of alternative connectivity on behavior of randomly constructed Boolean networks. Physica D. 170:2002;143-161.
23. Ravasz E., Somera A.L., Mongru D.A., Oltvai Z.N., Barabási A.-L., Hierarchical organization of modularity in metabolic networks. Science. 297:2002;1551-1555.
24. Solé R.V., Montoya J.M., Complexity and fragility in ecological networks. Proc. Roy. Soc. Lond., Ser. B. 268:2001;2039-2045.
25. Solé R.V., Pastor-Satorras R., Smith E., Kepler T.B., A model of large-scale proteome evolution. Adv. Complex Syst. 5(1):2002;43-54.
26. Stauffer D., Evolution by damage spreading in Kauffman model. J. Stat. Phys. 74(56):1994;1293-1299.
27. Strogatz S.H., Exploring complex networks. Nature. 410:2001;268-276.