Self-organized critical random Boolean networks

Bartolo Luque; Fernando J. Ballesteros; Enrique M. Muro

doi:10.1103/PhysRevE.63.051913

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Self-organized critical random Boolean networks

Bartolo Luque, Fernando J. Ballesteros, and Enrique M. Muro

Centro de Astrobiología (CAB) INTA-CSIC, Carretera de Ajalvir km. 4, 28850 Torrejón de Ardoz, Madrid, Spain

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Phys. Rev. E 63, 051913 – Published 25 April, 2001

DOI: https://doi.org/10.1103/PhysRevE.63.051913

Abstract

Standard random Boolean networks display an order-disorder phase transition. We add to the standard random Boolean networks a disconnection rule that couples the control and order parameters. In this way, the system is driven to the critical line transition. Under the influence of perturbations the system points out self-organized critical behavior. Several numerical simulations have been done and compared with a proposed analytical treatment.

References (22)

S. A. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution (Oxford University Press, New York 1993).
S.A. Kauffman, J. Theor. Biol. 22, 437 (1969).
A. Bhattacharjya and S. Liang, Phys. Rev. Lett. 77, 1644 (1996).
U. Bastolla and G. Parisi, Physica D 115, 203 (1996); ibid.115, 219 (1996).
R. Albert and A.-L. Barabási, Phys. Rev. Lett. 84, 5660 (1998).
S.A. Kauffman, Sci. Am. 265, 78 (1991).
A.-L. Barabási and R. Albert, Science 286, 509 (1999).
S.N. Dorogovtsev and J.F.F. Mendes, Phys. Rev. E 62, 1842 (2000).
S. Bornholdt and K. Sneppen, Phys. Rev. Lett. 81, 236 (1998).
M. Paczuski, K.E. Bassler, and A. Corral, Phys. Rev. Lett. 84, 3185 (2000).
S. Bornholdt and T. Rohlf, Phys. Rev. Lett. 84, 6114 (2000).
K.E. Kürten, J. Phys. A 21, L615 (1988).
B. Luque and R.V. Solé, Phys. Rev. E 55, 257 (1997).
S. Maslov and Y.-C. Zhang, Phys. Rev. Lett. 75, 1550 (1995).
M. Paczuski, S. Maslov, and P. Bak, Phys. Rev. E 53, 414 (1996).
D. Sornette and I. Dornic, Phys. Rev. E 54, 3334 (1996).
P. Grassberger and Y.-C. Zhang, Physica A 224, 169 (1996).
D. Sornette, A. Johansen, and I. Dornic, J. Phys. I 5, 325 (1995).
B. Derrida, in Fundamental Problems in Statistical Mechanics VII, edited by H. van Beijeren (North-Holland, Amsterdam, 1990).
P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).
For reviews see P. Bak, How Nature Works (Copernicus, New York, 1996); H.J. Jensen, Self-Organized Criticality (Cambridge University Press, Cambridge, 1998).
B. Luque and R.V. Solé, Physica A 284, 33 (2000).

[c1] S. A. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution (Oxford University Press, New York 1993).

[c2] S.A. Kauffman, J. Theor. Biol. 22, 437 (1969).

[c3] A. Bhattacharjya and S. Liang, Phys. Rev. Lett. 77, 1644 (1996).

[c4] U. Bastolla and G. Parisi, Physica D 115, 203 (1996); ibid.115, 219 (1996).

[c5] R. Albert and A.-L. Barabási, Phys. Rev. Lett. 84, 5660 (1998).

[c6] S.A. Kauffman, Sci. Am. 265, 78 (1991).

[c7] A.-L. Barabási and R. Albert, Science 286, 509 (1999).

[c8] S.N. Dorogovtsev and J.F.F. Mendes, Phys. Rev. E 62, 1842 (2000).

[c9] S. Bornholdt and K. Sneppen, Phys. Rev. Lett. 81, 236 (1998).

[c10] M. Paczuski, K.E. Bassler, and A. Corral, Phys. Rev. Lett. 84, 3185 (2000).

[c11] S. Bornholdt and T. Rohlf, Phys. Rev. Lett. 84, 6114 (2000).

[c12] K.E. Kürten, J. Phys. A 21, L615 (1988).

[c13] B. Luque and R.V. Solé, Phys. Rev. E 55, 257 (1997).

[c14] S. Maslov and Y.-C. Zhang, Phys. Rev. Lett. 75, 1550 (1995).

[c15] M. Paczuski, S. Maslov, and P. Bak, Phys. Rev. E 53, 414 (1996).

[c16] D. Sornette and I. Dornic, Phys. Rev. E 54, 3334 (1996).

[c17] P. Grassberger and Y.-C. Zhang, Physica A 224, 169 (1996).

[c18] D. Sornette, A. Johansen, and I. Dornic, J. Phys. I 5, 325 (1995).

[c19] B. Derrida, in Fundamental Problems in Statistical Mechanics VII, edited by H. van Beijeren (North-Holland, Amsterdam, 1990).

[c20] P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).

[c21] For reviews see P. Bak, How Nature Works (Copernicus, New York, 1996); H.J. Jensen, Self-Organized Criticality (Cambridge University Press, Cambridge, 1998).

[c22] B. Luque and R.V. Solé, Physica A 284, 33 (2000).

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Self-organized critical random Boolean networks

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References (22)

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