Berlin 2008 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 3: Statistical physics of complex networks I

DY 3.2: Vortrag

Montag, 25. Februar 2008, 10:45–11:00, A 053

The Phase Diagram of Random Threshold Networks — •Agnes Szejka, Tamara Mihaljev, and Barbara Drossel — Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, 64289 Darmstadt, Germany

Threshold networks are used as models for neural or gene regulatory networks. They show a rich dynamical behavior with a transition between a frozen and a chaotic phase. We investigate the phase diagram of randomly connected threshold networks with real-valued thresholds h and a fixed number of input nodes per node. The nodes are updated according to the same rules as in a model of the cell-cycle network of Saccharomyces cereviseae [PNAS 101, 4781 (2004)], which successfully reproduces the overall dynamical properties of the real network. Using the annealed approximation, we derive expressions for the time evolution of the proportion of active nodes in the network and for the average sensitivity of nodes to changes of the states of their input nodes. The results are compared with simulations of quenched networks. We find that the fact that with this update schema nodes do not change their state when the sum of their inputs is equal to the threshold value, leads to deviations of the dynamical behavior of quenched systems from the one predicted by the annealed approximation.