Chemical Networks with Inflows and Outflows: A Positive Linear Differential Inclusions Approach

摘要

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.