On the dynamics of two particular classes of Boolean automata networks: Boolean automata circuits and OR networks

The work presented here is set in line with fields of theoretical computer science and biology that study Boolean automata networks frequently seen as models of genetic regulation networks. In the context of biological regulation, former studies have highlighted the importance of circuits on the asymptotic dynamical behaviour of regulation networks. This is why we first chose to concentrate on networks whose underlying interaction graphs are circuits, that is, Boolean automata circuits. Here, we examine the dynamical behaviour of these networks in the case of a synchronous update schedule of their automata as well as in that of more general update schedules such as sequential or block sequential update schedules. Next, driven by the will to develop our understanding of networks with arbitrary underlying structures, we focus on OR networks and give some properties of their dynamics in an attempt to fully classify these networks according to their asymptotic dynamical behaviour considering all of their synchronous, sequential and block sequential update schedules.