Criticality in random threshold networks: annealed approximation and beyond

Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity K c . In this type of model—contrary to Boolean Networks—propagation of local pertur...

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Bibliographic Details
Published in:Physica A 2002-07, Vol.310 (1), p.245-259
Main Authors: Rohlf, Thimo, Bornholdt, Stefan
Format: Article
Language:English
Subjects:
Complex systems
Critical properties
Networks
Percolation
Phase transitions
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Summary:Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity K c . In this type of model—contrary to Boolean Networks—propagation of local perturbations (damage) depends on the in-degree of the sites. K c is determined analytically, using an annealed approximation, and the results are confirmed by numerical simulations. It is shown that the statistical distributions of damage spreading near the percolation transition obey power-laws, and dynamical correlations between active network clusters become maximal. We investigate the effect of local damage suppression at highly connected nodes for networks with scale-free in-degree distributions. Possible relations of our findings to properties of real-world networks, like robustness and non-trivial degree-distributions, are discussed.
ISSN:0378-4371
1873-2119
DOI:10.1016/S0378-4371(02)00798-7