Positive circuits and maximal number of fixed points in discrete dynamical systems
| dc.creator | Richard, Adrien | |
| dc.date | 2008-07-26 | |
| dc.date | 2008-12-01 | |
| dc.date.accessioned | 2026-07-07T12:05:56Z | |
| dc.date.available | 2026-07-07T12:05:56Z | |
| dc.description | We 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.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0807.4229 | |
| dc.identifier | http://arxiv.org/abs/0807.4229 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208513 | |
| dc.subject | Discrete Mathematics | |
| dc.subject | G.2.1; G.2.2; F.1.1 | |
| dc.title | Positive circuits and maximal number of fixed points in discrete dynamical systems | |
| dc.type | text |