Geodesic
An Invariant-Manifold Approach to Lumping
B. E. Okeke1 ; M. R. Roussel1
1 Department of Chemistry and Biochemistry, University of Lethbridge Lethbridge, Alberta T1K 3M4, Canada
Mathematical modelling of natural phenomena, Tome 10 (2015) no. 3, pp. 149-167

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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.
DOI : 10.1051/mmnp/201510312

B. E. Okeke 1 ; M. R. Roussel 1

1 Department of Chemistry and Biochemistry, University of Lethbridge Lethbridge, Alberta T1K 3M4, Canada 
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B. E. Okeke; M. R. Roussel. An Invariant-Manifold Approach to Lumping. Mathematical modelling of natural phenomena, Tome 10 (2015) no. 3, pp. 149-167. doi: 10.1051/mmnp/201510312

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