ArticleNonlinear dynamics2024
Bifurcations in planar, quadratic mass-action networks with few reactions and low molecularity.
Article in Nonlinear dynamics, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Positive equilibria in mass action networks: geometry and bounds.Journal of mathematical biology · 2026Article
- The Inheritance of Local Bifurcations in Mass Action Networks.Journal of nonlinear science · 2025Article
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Abstract
In this paper we study bifurcations in mass-action networks with two chemical species and reactant complexes of molecularity no more than two. We refer to these as planar, quadratic networks as they give rise to (at most) quadratic differential equations on the nonnegative quadrant of the plane. Our aim is to study bifurcations in networks in this class with the fewest possible reactions, and the lowest possible product molecularity. We fully characterise generic bifurcations of positive equilibria in such networks with up to four reactions, and product molecularity no higher than three. In these networks we find fold, Andronov-Hopf, Bogdanov-Takens and Bautin bifurcations, and prove the non-occurrence of any other generic bifurcations of positive equilibria. In addition, we present a number of results which go beyond planar, quadratic networks. For example, we show that mass-action networks without conservation laws admit no bifurcations of codimension greater than
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