## Preprint 2010-11

## Julio Aracena, Luis Gomez, Lilian Salinas:

### Limit cycles and update digraphs in Boolean networks

### Abstract:

Deterministic Boolean networks (BNs) have been used as models of gene regulation and other biological networks. One key element in these models is the update schedule, which indicates the order in which states have to be updated. In Aracena et. al. (2009) equivalence classes of deterministic update schedules according to the labeled digraph associated to a BN (update digraph) were defined. It was proved that two schedules in the same class yield the same dynamical behavior of a given BN. In this paper we study the relationships between the update digraphs and the preservation of limit cycles of BNs which differ only in the update schedules. We exhibite necessary conditions in the connection digraph architecture in order to preserve limit cycles. Besides, we construct some update schedule classes whose elements yield a same limit cycle under certain conditions.

This preprint gave rise to the following definitive publication(s):

**Julio ARACENA, Luis GOMEZ, Lilian SALINAS: ***Limit cycles and update digraphs in Boolean networks*. Discrete Applied Mathematics, vol. 161, 1-2, pp. 1-12, (2013).