Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 3: Statistical physics of complex networks I
DY 3.3: Vortrag
Montag, 25. Februar 2008, 11:00–11:15, A 053
The Critical Line in Random Threshold Networks with Inhomogeneous Thresholds — •Thimo Rohlf — Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA — Max-Planck Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig
We calculate analytically the critical connectivity Kc of Random Threshold Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the results by numerical simulations. We find a super-linear increase of Kc with the (average) absolute threshold |h|, which approaches Kc(|h|) ∼ h2/(2ln|h|) for large |h|, and show that this asymptotic scaling is universal for RTN with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than h2. Interestingly, we find that inhomogeneous distribution of thresholds leads to increased propagation of perturbations for sparsely connected networks, while for densely connected networks damage is reduced; the cross-over point yields a novel, characteristic connectivity Kd. Further, damage propagation in RTN with in-degree distributions that exhibit a scale-free tail kinγ is studied; we find that a decrease of γ can lead to a transition from supercritical (chaotic) to subcritical (ordered) dynamics. Last, local correlations between node thresholds and in-degree are introduced. Here, numerical simulations show that even weak (anti-)correlations can lead to a transition from ordered to chaotic dynamics, and vice versa. Interestingly, in this case the annealed approximation fails to predict the dynamical behavior for sparse connectivities K, even for large networks with N > 104 nodes.