Chemical networks with inflows and outflows: a positive linear differential inclusions approach.
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.
Angeli
David
D
Dept. of Electrical and Electronic Engineering, Imperial College, London, UK. angeli@dsi.unifi.it
De Leenheer
Patrick
P
Sontag
Eduardo D
ED
D000465:Algorithms; D055598:Chemical Phenomena; D003198:Computer Simulation; D007700:Kinetics; D008956:Models, Chemical