Dynamics in Random Boolean Networks

TL;DRAbstract

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

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