Invariant manifold methods for metabolic model reduction.
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.
Roussel
Marc R.
MR
Department of Chemistry and Biochemistry, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada.
Fraser
Simon J.
SJ