Topological fixed points in Boolean networks

Loïc Paulevé (1) , Adrien Richard (2)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 I3S - Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis

We introduce the notion of a topological fixed point in Boolean Networks: a fixed point of Boolean network F is said to be topologic if it is a fixed point of every Boolean network with the same interaction graph as the one of F. Then, we characterize the number of topological fixed points of a Boolean network according to the structure of its interaction graph.

Mots clés: boolean network; fixed point; interaction graph

Domaines: Combinatoire [math.CO]; Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Loïc Paulevé, Adrien Richard. Topological fixed points in Boolean networks. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2010, 348 (15-16), pp.825-828. ⟨10.1016/j.crma.2010.07.014⟩. ⟨hal-00510892⟩