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標題: Investigation of the dynamics of critical k=2 Kauffman networks using second-order loops
作者: Chen, S.T.
Tseng, H.C.
Wang, S.C.
Li, P.C.
關鍵字: Boolean update functions;Kauffman networks;network dynamics;relevant;element;second-order loop;random boolean networks;automata
Project: Journal of the Physical Society of Japan
期刊/報告no:: Journal of the Physical Society of Japan, Volume 77, Issue 9.
The mean number and length of attractors in Kauffman networks are strongly affected by the loops formed from the relevant elements. In this paper, to investigate the dynamic behavior of the critical k = 2 Kauffman networks, we first employ second-order loops. viz., the relevant element loops having, two elements each with two inputs. On the basis of our simulation, in addition to obtaining various dynamic properties of the second-order loops, we also unexpectedly find that the dynamic behavior of the second-order loops is similar to that of the Kauffman networks. Thus, we were able to speculate oil various properties of Kauffman networks Using the results obtained from the second-order loops. It turns out that for the second-order loops. the mean number of attractors increases exponentially with the number of relevant elements. while the mean attractor length increases as a power law with the number of relevant elements.
ISSN: 0031-9015
DOI: 10.1143/jpsj.77.094002
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