Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 29: Poster II
DY 29.29: Poster
Donnerstag, 28. Februar 2008, 16:00–18:00, Poster C
Perturbation propagation in random and non-random Boolean Networks — •Christoph Fretter1,2, Agnes Szejka1, and Barbara Drossel1 — 1Institut für Festkörperphysik, Technische Universität Darmstadt, Deutschland — 2Institut für Informatik, Martin-Luther-Universität Halle-Wittenberg, Deutschland
According to Derrida's definition of criticality, networks in which the perturbation of a single node propagates on an average to more (less) than one other node are chaotic (frozen). At the boundary between these two phases are critical networks. For Random Boolean Networks, the phase diagram can be derived analytically by considering the connectivity of the networks and the chosen update functions, and by using the annealed approximation. This consideration can be generalised to the Derrida plot, in which perturbations of all sizes are considered, and their value one time step later is evaluated.
By introducing a modification of this Derrida plot, we show that even Random Boolean Networks with a small size agree well with the results obtained by the annealed approximation, but non-random networks show a very different behaviour. We focus on networks that were evolved for high dynamical robustness. The most important conclusion is that the simple distinction between frozen, critical and chaotic networks is no longer useful, since such evolved networks can display properties of both frozen and chaotic networks.