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

Niclas Kruff Sebastian Walcher

*Corresponding author: Sebastian Walcher walcher@matha.rwth-aachen.de

MBE2019,5,5062doi:10.3934/mbe.2019255

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.

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