Positive circuits and maximal number of fixed points in discrete dynamical systems

dc.creatorRichard, Adrien
dc.date2008-07-26
dc.date2008-12-01
dc.date.accessioned2026-07-07T12:05:56Z
dc.date.available2026-07-07T12:05:56Z
dc.descriptionWe consider the Cartesian product X of n finite intervals of integers and a map F from X to itself. As main result, we establish an upper bound on the number of fixed points for F which only depends on X and on the topology of the positive circuits of the interaction graph associated with F. The proof uses and strongly generalizes a theorem of Richard and Comet which corresponds to a discrete version of the Thomas' conjecture: if the interaction graph associated with F has no positive circuit, then F has at most one fixed point. The obtained upper bound on the number of fixed points also strongly generalizes the one established by Aracena et al for a particular class of Boolean networks.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/0807.4229
dc.identifierhttp://arxiv.org/abs/0807.4229
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208513
dc.subjectDiscrete Mathematics
dc.subjectG.2.1; G.2.2; F.1.1
dc.titlePositive circuits and maximal number of fixed points in discrete dynamical systems
dc.typetext

Files

Collections