title: Chemical networks with inflows and outflows: a positive linear differential inclusions approach.
abstract: Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle.
authors.affiliation: Dept. of Electrical and Electronic Engineering, Imperial College, London, UK. angeli@dsi.unifi.it
authors.forename: David
authors.initials: D
authors.lastname: Angeli
authors.forename: Patrick
authors.initials: P
authors.lastname: De Leenheer
authors.forename: Eduardo D
authors.initials: ED
authors.lastname: Sontag
mesh_terms: D000465:Algorithms; D055598:Chemical Phenomena; D003198:Computer Simulation; D007700:Kinetics; D008956:Models, Chemical