WIAS Preprint No. 532, (1999)

Local state space reduction of multi-scale systems


  • Handrock-Meyer, Sybille
  • Schneider, Klaus R.

2010 Mathematics Subject Classification

  • 34E15 92E20


  • state space reduction, multi-scale systems, singularly perturbed systems, reaction kinetics




Modelling reaction kinetics in a homogeneous medium usually leads to stiff systems of ordinary differential equations the dimension of which can be large. A well-known approach to reduce the dimension of such systems is the quasi-steady state assumption (QSSA): the derivative of fast variables is assumed to be zero. This procedure requires some knowledge of the underlying chemistry, moreover the corresponding differential system must be explicitly given. In this paper we shall describe and justify a procedure for a local reduction of the dimension of state space which does not require chemical insight as well as an explicit knowledge of the system in a singularly perturbed form. The mathematical justification is based on the theory of invariant manifolds.

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