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arXiv · 2202.11034

Some minimal bimolecular mass-action systems with limit cycles

Balázs Boros·Josef Hofbauer
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Abstract

We discuss three examples of bimolecular mass-action systems with three species, due to Feinberg, Berner, Heinrich, and Wilhelm. Each system has a unique positive equilibrium which is unstable for certain rate constants and then exhibits stable limit cycles, but no chaotic behaviour. For some rate constants in the Feinberg--Berner system, a stable equilibrium, an unstabe limit cycle, and a stable limit cycle coexist. All three networks are minimal in some sense. By way of homogenising the above three examples, we construct bimolecular mass-conserving mass-action systems with four species that admit a stable limit cycle. The homogenised Feinberg--Berner system and the homogenised Wilhelm--Heinrich system admit the coexistence of a stable equilibrium, an unstable limit cycle, and a stable limit cycle.

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Balázs Boros, Josef Hofbauer. 2022-09-13. Some minimal bimolecular mass-action systems with limit cycles. https://doi.org/10.1016/j.nonrwa.2023.103839

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