Asymptotic expansions of slow invariant manifolds and reduction of chemical kinetics models

Abstract

Methods of the geometric theory of singular perturbations are used to reduce the dimen sions of problems in chemical kinetics. The methods are based on using slow invariant manifolds. As a result, the original system is replaced by one on an invariant manifold, whose dimension coincides with that of the slow subsystem. Explicit and implicit representations of slow invariant manifolds are applied. The mathematical apparatus described is used to develop N.N. Semenov's fundamental ideas related to the method of quasi stationary concentrations and is used to study particular problems in chemical kinetics.

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“…The critical regime separating the basic types of the regimes, slow and relaxation, was modelled with the help of the integral manifolds of variable stability. This approach was used in [13][14][15][16][17][18][19][20][21][22][23] for modelling of the critical phenomena in chemical systems.…”

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