Criticality in Random Threshold Networks: Annealed Approximation and Beyond

Thimo Rohlf; Stefan Bornholdt

doi:10.1016/s0378-4371(02)00798-7

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Criticality in Random Threshold Networks: Annealed Approximation and Beyond

Thimo Rohlf·Stefan Bornholdt

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Abstract

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.

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BibTeX RIS

Thimo Rohlf, Stefan Bornholdt. 2002-01-07. Criticality in Random Threshold Networks: Annealed Approximation and Beyond. https://doi.org/10.1016/s0378-4371(02)00798-7

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