Dresden 2006 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.90: Poster
Donnerstag, 30. März 2006, 16:00–18:00, P1
Stability of attractors under noisy delays in Boolean networks — •Konstantin Klemm1 and Stefan Bornholdt2 — 1Dept. of Bioinformatics, University of Leipzig, Germany — 2Institute for Theoretical Physics, University of Bremen, Germany
Boolean networks at the critical point have been discussed for many years as, e.g., scaling of number of attractors with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a common earlier expectation of sublinear scaling. We here point out that these results are obtained using deterministic synchronous update, which limits their significance for biological systems where noise is omnipresent.
We check the stability of the attractors when the assumption of synchronous update is relaxed. The synchrony in the model is perturbed 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 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, the number of stable attractors grows sublinearly with increasing system size [1]. Thus in large systems almost all attractors considered earlier are artefacts arising from the synchronous clocking mode.
[1] K. Klemm and S. Bornholdt, Phys. Rev. E (R), in press (2005), e-print cond-mat/0411102