Dresden 2006 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 46: Poster

DY 46.89: Poster

Donnerstag, 30. März 2006, 16:00–18:00, P1

Scaling in critical random Boolean networks with different connectivity and different choice of update functions — •Tamara Mihaljev, Barbara Drossel, and Viktor Kaufman — Institut für Festkörperphysik, Technische Universität Darmstadt

The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behaviour for “critical” parameter values at the boundary between a frozen and a disordered phase, and is therefore used for studies of real network problems. We consider here the general class of critical Kauffman networks with different number of inputs per node and different distributions of Boolean functions. By defining and analyzing two different stochastic processes we derive mostly analytically the scaling behaviour of the number of nonfrozen and relevant nodes in these networks in the thermodynamic limit. Our results show that only a finite number of relevant nodes have more than one relevant input. It follows that for every class of critical Kauffman networks all relevant components apart from a finite number are simple loops and that the mean number and length of attractors increases faster than any power law with network size.