Dynamics and evolution of random Boolean networks [Elektronische Ressource] / von Tamara Mihaljev

Dynamics and Evolution of Random BooleanNetworksVom Fachbereich Physikder Technischen Universit¨at Darmstadtzur Erlangung des Gradeseines Doktors der Naturwissenschaften(Dr. rer. nat.)genehmigteD i s s e r t a t i o nvonDipl.-Phys. Tamara Mihaljevaus Pula, KroatienReferentin: Prof. Dr. Barbara DrosselKorreferent: Prof. Dr. Markus PortoTag der Einreichung: 14.10.2008Tag der mu¨ndlichen Pru¨fung: 10.11.2008Darmstadt 2008D17iiMojim roditeljimaivAbstractRandom Boolean networks are used as generic models for the dynamics of complexsystems of interacting entities, such as social and economic networks, neural net-works, and gene or protein interaction networks. The model studied in this thesiswas introduced by S. Kauffman as a simple model for gene regulation. The systemconsists of N nodes, each of which receives inputs from K randomly chosen nodes.The state of a node is a Boolean function of the states of its input nodes. The func-tions are assigned to the nodes at random, and the states of all nodes in a networkare updated in parallel. Asymptotic dynamical states of a network are representedby attractors in state space. Thus, their number and lengths are important featuresof the networks. The nodes in a network can be classified as frozen, irrelevant, orrelevant, according to their dynamics onanattractor. Therelevant nodesdeterminecompletely the number and the period of attractors.