Tikhonov–Fenichel reductions and their application to a novel modelling approach for mutualism

Johannes Apelt and Volkmar Liebscher

Theoretical Population Biology, 2025, vol. 166, issue C, 16-35

Abstract: When formulating a model there is a trade-off between model complexity and (biological) realism. In the present paper we demonstrate how model reduction from a precise mechanistic “super model†to simpler conceptual models using Tikhonov–Fenichel reductions, an algebraic approach to singular perturbation theory, can mitigate this problem. Compared to traditional methods for time scale separations (Tikhonov’s theorem, quasi-steady state assumption), Tikhonov–Fenichel reductions have the advantage that we can compute a reduction directly for a separation of rates into slow and fast ones instead of a separation of components of the system. Moreover, we can find all such reductions algorithmically.

Keywords: Tikhonov–Fenichel reduction; Time scale separation; Singular perturbation theory; Super model; Mutualism (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0040580925000528
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:166:y:2025:i:c:p:16-35

DOI: 10.1016/j.tpb.2025.08.004

Access Statistics for this article

Theoretical Population Biology is currently edited by Jeremy Van Cleve

More articles in Theoretical Population Biology from Elsevier
Bibliographic data for series maintained by Catherine Liu ().