ArticleBulletin of mathematical biology2023
Chemical Systems with Limit Cycles.
Article in Bulletin of mathematical biology, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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1 citing paper in PubMed, 7 citations in OpenAlex.
- Planar chemical reaction systems with algebraic and non-algebraic limit cycles.Journal of mathematical biology · 2025Article
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2 authors at 2 institutions in 3 countries.
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Abstract
The dynamics of a chemical reaction network (CRN) is often modeled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of concentrations of chemical species involved. Given an arbitrarily large integer [Formula: see text], we show that there exists a CRN such that its ODE model has at least K stable limit cycles. Such a CRN can be constructed with reactions of at most second-order provided that the number of chemical species grows linearly with K. Bounds on the minimal number of chemical species and the minimal number of chemical reactions are presented for CRNs with K stable limit cycles and at most second order or seventh-order kinetics. We also show that CRNs with only two chemical species can have K stable limit cycles, when the order of chemical reactions grows linearly with K.
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