Coordinate-independent singular perturbation reduction for systems with three time scales

Abstract

On the basis of recent work by Cardin and Teixeira on ordinary differential equations with more than two time scales, we devise a coordinate-independent reduction for systems with three time scales; thus no a priori separation of variables into fast, slow etc. is required. Moreover we consider arbitrary parameter dependent systems and extend earlier work on Tikhonov-Fenichel parameter values -- i.e. parameter values from which singularly perturbed systems emanate upon small perturbations -- to the three time-scale setting. We apply our results to two standard systems from biochemistry.

References in corpus (1)

• Singular perturbations and scaling

Cited by in corpus (3)

• Algorithmic Reduction of Biological Networks With Multiple Time Scales
• Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems
• Multiple timescales and the parametrisation method in geometric singular perturbation theory