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

Niclas Kruff; Sebastian Walcher; Niclas Kruff; Sebastian Walcher

doi:10.3934/mbe.2019255

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 5062-5091. doi: 10.3934/mbe.2019255

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

Niclas Kruff ,
Sebastian Walcher ^,

Mathematik A, RWTH Aachen, 52056 Aachen, Germany

Received: 28 March 2019 Accepted: 13 May 2019 Published: 03 June 2019

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.

Keywords:

Citation: Niclas Kruff, Sebastian Walcher. Coordinate-independent singular perturbation reduction for systems with three time scales[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 5062-5091. doi: 10.3934/mbe.2019255

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Abstract

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