Complex Systems

Recent Results on Ordering Parameters in Boolean Networks Download PDF

Jürgen Klüver
Electronic mail address: juergen.kluever@uni-due.de

Jörn Schmidt
University of Duisburg-Essen, FB2,
Campus Essen,
Universitätsstr. 12,
45117 Essen, Germany

Abstract

The dynamics of discrete mathematical systems can be related to the values of certain ordering parameters. Experiments with the total set of possible structures of a boolean network with six elements and extended sets of two-valued boolean functions show that three simple parameters describing the topology, the bias of boolean functions, and their canalyzing potential yield necessary conditions for complex dynamics. The crucial factor determining dynamics turns out to be the topology. The impact on simulations of real systems is discussed.