Berlin 2005 – scientific programme
Parts | Days | Selection | Search | Downloads | Help
DY: Dynamik und Statistische Physik
DY 21: Statistical Physics in Biological Systems
DY 21.9: Talk
Saturday, March 5, 2005, 10:30–10:45, TU H2032
Stable and unstable attractors in critical Boolean networks — •Konstantin Klemm1 and Stefan Bornholdt2 — 1Bioinformatik, Universität Leipzig, Kreuzstr. 7b, 04103 Leipzig — 2Theoretische Physik, Universität Bremen, Otto-Hahn-Allee, 28334 Bremen
Studying the dynamics of Boolean networks, we check the stability of the attractors against small perturbations. We perturb the synchrony in the model by slightly accelerating or decelerating the update of a subset of units. This set of perturbations is motivated by the noisy delay time with which a biological switch (neuron, expressed gene) responds to a changing input. An attractor is called stable if after any such perturbation synchrony is regained. In random Boolean networks at the critical point (connectivity K=2) the number of stable attractors grows sublinearly with increasing system size [1], while the growth of the total number of attractors is superpolynomial. Thus in large systems almost all attractors considered earlier are artefacts arising from the synchronous clocking mode.
[1] K. Klemm and S. Bornholdt, preprint cond-mat/0411102