title: Invariant manifold methods for metabolic model reduction.
abstract: After the decay of transients, the behavior of a set of differential equations modeling a chemical or biochemical system generally rests on a low-dimensional surface which is an invariant manifold of the flow. If an equation for such a manifold can be obtained, the model has effectively been reduced to a smaller system of differential equations. Using perturbation methods, we show that the distinction between rapidly decaying and long-lived (slow) modes has a rigorous basis. We show how equations for attracting invariant (slow) manifolds can be constructed by a geometric approach based on functional equations derived directly from the differential equations. We apply these methods to two simple metabolic models. (c) 2001 American Institute of Physics.
authors.affiliation: Department of Chemistry and Biochemistry, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada.
authors.forename: Marc R.
authors.initials: MR
authors.lastname: Roussel
authors.forename: Simon J.
authors.initials: SJ
authors.lastname: Fraser