Oscillations in Planar Deficiency-One Mass-Action Systems
Balázs Boros, Josef Hofbauer
TL;DR
This paper explores how certain chemical reaction systems can exhibit oscillations when they have a specific structural property called deficiency-one.
Contribution
The paper introduces new examples of planar deficiency-one mass-action systems that show oscillatory behavior, such as centers or multiple limit cycles.
Findings
Deficiency-one planar mass-action systems can exhibit oscillatory dynamics like centers or multiple limit cycles.
These findings contrast with deficiency-zero systems, which always have globally stable equilibria.
The paper provides concrete examples to illustrate the diverse behaviors of deficiency-one systems.
Abstract
Whereas the positive equilibrium of a planar mass-action system with deficiency zero is always globally stable, for deficiency-one networks there are many different scenarios, mainly involving oscillatory behaviour. We present several examples, with centers or multiple limit cycles.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Gene Regulatory Network Analysis · Mathematical Biology Tumor Growth