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Chemical networks with inflows and outflows: a positive linear differential inclusions approach
David Angeli1, Patrick De Leenheer, Eduardo D Sontag
1Dept. of Electrical and Electronic Engineering, Imperial College, London, UK. angeli@dsi.unifi.it
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.
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