title: Time Hierarchies and Model Reduction in Canonical Non-linear Models.
abstract: The time-scale hierarchies of a very general class of models in differential equations is analyzed. Classical methods for model reduction and time-scale analysis have been adapted to this formalism and a complementary method is proposed. A unified theoretical treatment shows how the structure of the system can be much better understood by inspection of two sets of singular values: one related to the stoichiometric structure of the system and another to its kinetics. The methods are exemplified first through a toy model, then a large synthetic network and finally with numeric simulations of three classical benchmark models of real biological systems.
authors.affiliation: Specialty Division for Systems Biotechnology, Technische Universität München Garching, Germany.
authors.forename: Hannes
authors.initials: H
authors.lastname: Löwe
authors.affiliation: Specialty Division for Systems Biotechnology, Technische Universität München Garching, Germany.
authors.forename: Andreas
authors.initials: A
authors.lastname: Kremling
authors.affiliation: Specialty Division for Systems Biotechnology, Technische Universität München Garching, Germany.
authors.forename: Alberto
authors.initials: A
authors.lastname: Marin-Sanguino
keywords: biochemical systems theory; mathematical modeling; model reduction; quasi-polynomial systems; systems biology; time-scales