Abstract
A study is made of the spreading of damage in the random but deterministic Kauffman model on the square lattice with the spreading from one edge of the lattice. The critical value of the parameterp c above which the system becomes chaotic is found to bep c≈0.298. The possibility of suppression of the chaotic phase by noise is also studied. It is found that forp⩾p c, an extremely large noise levelg>0.99 is required, if possible at all.
References
S. A. Kauffman,J. Theor. Biol. 22:437 (1969).
S. A. Kauffman,Physica D 10:145 (1984).
B. Derrida and Y. Pomeau,Europhys. Lett. 1:45 (1986).
B. Derrida and D. Stauffer,Europhys. Lett. 2:739 (1986).
G. Weisbuch and D. Stauffer,J. Phys. (Paris) 48:11 (1987).
D. Stauffer, in Proceedings of the Conference “The Physics of Disordered Systems,” Bar Ilan University,Phil. Mag., to be published.
B. Derrida, in Proceedings of the Conference “The Physics of Disordered Systems,” Bar Ilan University,Phil. Mag., to be published.
P. Grassberger,J. Phys. A 19:1681 (1986).
D. Stauffer,Introduction to Percolation Theory (1985).
K. Kaneko and Y. Akutsu,J. Phys. A 19:L69 (1986).
Author information
Authors and Affiliations
Additional information
On leave from Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.
Rights and permissions
About this article
Cite this article
Lam, P.M. A percolation approach to the Kauffman model. J Stat Phys 50, 1263–1269 (1988). https://doi.org/10.1007/BF01019165
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01019165