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

Mathematical Biosciences and Engineering

Niclas Kruff¹  Sebastian Walcher¹ 

[1] Mathematik A, RWTH Aachen, 52056 Aachen, Germany;

关键词: reaction network;    dimension reduction;    invariant set;    multiple time scales;   

DOI  :  10.3934/mbe.2019255

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown