Dynamical Properties of Discrete Reaction Networks - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Biology Année : 2013

Dynamical Properties of Discrete Reaction Networks

Résumé

Reaction networks are commonly used to model the evolution of populations of species subject to transformations following an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete Reaction Networks (DRNs). DRNs can be seen as modelling the underlying discrete nondeterministic transitions of stochastic models of reactions networks. In that sense, any proof of non-reachability in DRNs directly applies to any concrete stochastic models, independently of kinetics laws and constants. Moreover, if stochastic kinetic rates never vanish, reachability properties are equivalent in the two settings. The analysis of two global dynamical properties of DRNs is addressed: irreducibility, i.e., the ability to reach any discrete state from any other state; and recurrence, i.e., the ability to return to any initial state. Our results consider both the verification of such properties when species are present in a large copy number, and in the general case. The obtained necessary and sufficient conditions involve algebraic conditions on the network reactions which in most cases can be verified using linear programming. Finally, the relationship of DRN irreducibility and recurrence with dynamical properties of stochastic and continuous models of reaction networks is discussed.
Fichier principal
Vignette du fichier
main.pdf (273.55 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00769448 , version 1 (01-01-2013)
hal-00769448 , version 2 (06-06-2013)

Identifiants

Citer

Loïc Paulevé, Gheorghe Craciun, Heinz Koeppl. Dynamical Properties of Discrete Reaction Networks. Journal of Mathematical Biology, 2013, pp.Online First, 1-18. ⟨10.1007/s00285-013-0686-2⟩. ⟨hal-00769448v2⟩
107 Consultations
204 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More