Dynamics in Random Boolean Networks

Abstract: There are many examples of complex networks in science. It can be genetic regulation in living cells, computers on the Internet, or social and economic networks. In this context, Boolean networks provide simplistic models that are relatively easy to handle using computer simulations and mathematical methods. A good understanding of Boolean networks may form a foundation to investigations of more complicated systems. In this thesis, I present research on randomly created Boolean networks, using both computer simulations and mathematical analysis. The analytical results are mainly focused on the number of attractors in random Boolean networks. These results give interesting implications to Kauffman's analogy between cell types and attractors in random Boolean networks. Also, a mathematical technique is developed to investigate networks with one input per node. Such networks are strongly related to more complicated random Boolean networks and to random maps. Furthermore, Boolean networks are constructed with guidance of experimental data on genetic regulation. Data from gene regulatory connections in yeast provide a network architecture, and compiled data on gene regulatory interactions form the basis for a distribution of nested canalyzing Boolean rules. Stability issues in such networks are addressed and a simplistic model of cells in a tissue is investigated.