Regensburg 2007 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 30: Poster II

DY 30.15: Poster

Donnerstag, 29. März 2007, 16:00–18:00, Poster D

Random Boolean Networks with noise — •Christoph Fretter and Barbara Drossel — Institut für Festkörperphysik, Technische Universität Darmstadt, Deutschland

Boolean networks are used as a model for gene regulation networks, where stochastic fluctuations are ubiquitous due to small molecule concentrations. We investigate the influence of stochastic noise on the dynamics of Boolean networks. Noise is implemented in terms of a “temperature”, i.e., a probability that a node is assigned a random state instead of following the deterministic update rule. We measure the robustness of the network dynamics against noise by evaluating the probability of returning to the same attractor after the noise has acted for a finite time. The parameters to be varied are the noise strength, the network size and network topology, and the set of update functions used. We show that under weak noise even simple networks display nontrivial behaviour. We use the theory of relevant components to extrapolate the results to large networks. The methods used are numerical simulations as well as analytical calculations.