Model reduction by extended quasi-steady-state approximation

We extend the quasi-steady-state approximation (QSSA) with respect to the class of differential systems as well as with respect to the order of approximation. We illustrate the first extension by an example which cannot be treated in the frame of the classical approach. As an application of the second extension we prove that the trimolecular autocatalator can be approximated by a fast bimolecular reaction system. Finally we describe a class of singularly perturbed systems for which a higher order QSSA can easily be obtained.