Tikhonov's Theorem and Quasi-Steady State
By Lena Noethen, Sebastian Walcher. 2011
55 citations recorded by the source corpus.
There exists a systematic approach to asymptotic properties for quasi-steady state phenomena via the classical theory of Tikhonov and Fenichel. This observation allows, on the one hand, to settle convergence issues, which are far from trivial in asymptotic expansions. On the other hand, even if one takes convergence for granted, the approach yields a natural way to compute a reduced system on the slow manifold, with a reduced equation that is frequently simpler than the one obtained by the ad hoc approach. In particular, the reduced system is always rational. The paper includes a discussion of necessary and sufficient conditions for applicability of Tikhonov's and Fenichel's theorems, computational issues and a direct determination of the reduced system. The results are applied to several relevant examples.
Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/be3b8fa77d4f0601945a1985b7aab3f7c342d985
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Control and Systems Engineering
In Statistical and Nonlinear Physics
Citations in the corpus
- A constructive approach to quasi-steady state reductions (2014, methodology): “For general differential equations with rational right-hand side, the principal result in [26] states that whenever the hypotheses of Tikhonov’s theorem are satisfied (for suitable coordinates which need not be known explicitly), there exists a reduced system which has again rational righthand side.”
- Determining “small parameters” for quasi-steady state (2015, background): “However, additional conditions ensure sufficiency; see [34], Prop.”