Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 14: Networks: From Topology to Dynamics I (joint session of BP, DY, SOE)

DY 14.1: Talk

Wednesday, March 24, 2010, 10:15–10:30, H44

Stability of continuous vs. Boolean dynamics — •Fakhteh Ghanbarnejad and Konstantin Klemm — Department of Bioinformatics, University of Leipzig, Germany

Boolean networks are time- and state-discrete models of dynamical systems with many variables and quenched disorder in the couplings. The use of such discrete models makes large systems amenable to detailed analysis. The discretization, however, may bring about “artificial” behavior not found in the continuous description with differential equations. The usual definition of Boolean attractor stability is based on flipping the state of single nodes and checking if the system returns to the attractor, similar to a damage spreading scenario. This stability concept, however, does not reflect the stability of limit cycles in the corresponding continuous system of delay differential equations. Here we have a fresh look at the correspondence of stability definitions in continuous and discrete dynamics. We run extensive numerical simulations to test stability on various system architectures (networks). We establish a criterion for assessing stability of the continuous dynamics by probing the discrete counterpart.