Math. Model. Nat. Phenom.
Volume 10, Number 3, 2015Model Reduction
|Page(s)||149 - 167|
|Published online||22 June 2015|
An Invariant-Manifold Approach to Lumping
Department of Chemistry and Biochemistry, University
of Lethbridge Lethbridge, Alberta
Corresponding author. E-mail: firstname.lastname@example.org
Differential equation models of chemical or biochemical systems usually display multiple, widely varying time scales, i.e. they are stiff. After the decay of transients, trajectories of these systems approach low-dimensional invariant manifolds on which the eventual attractor (an equilibrium point in a closed system) is approached, and in which this attractor is embedded. Computing one of these slow invariant manifolds (SIMs) results in a reduced model of dimension equal to the dimension of the SIM. Another approach to model reduction involves lumping, the formulation of a reduced set of variables that combine the original model variables and in terms of which the reduced model is framed. In this study, we combine lumping with a constructive method for SIMs based on the iterative solution of the invariance equation. We illustrate these methods using a simple model of a linear metabolic pathway, and a model for hydrogen oxidation. The former is treated with a linear lumping function, while a nonlinear lumping function based on a Lyapunov function is used in the latter.
Mathematics Subject Classification: 80A30 / 92C45 / 34C45
Key words: model reduction / slow invariant manifold / lumping / metabolic modeling / combustion modeling
© EDP Sciences, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.