https://doi.org/10.1140/epjb/e2004-00260-4
Dynamics of threshold network on non-trivial distribution degree
Sony Corporation, 2-10-14 Osaki, Shinagawa, Tokyo, Japan
Corresponding author: a ikuo@arch.sony.co.jp
Received:
25
February
2004
Published online:
12
August
2004
The dynamics of a threshold network (TN) with thermal noise on scale-free, random-graph, and small-world topologies are considered herein. The present analytical study clarifies that there is no phase transition independent of network structure if temperature T=0, threshold h=0 and the probability distribution degree P(k) satisfies P(0)=D=0. The emergence of phase transition involving three parameters, T, h and D is also investigated. We find that a TN with moderate thermal noise extends the regime of ordered dynamics, compared to a TN in the T=0 regime or a Random Boolean Network (RBN). A TN can be continuously reduced to an expression of RBN in the infinite T limit.
PACS: 89.75.Fb – Structures and organization in complex systems / 89.20.Hh – World Wide Web, Internet / 05.70.Fh – Phase transitions: general studies
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004
