Some minimal bimolecular mass-action systems with limit cycles
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.
Cite
@article{arxiv.2202.11034,
title = {Some minimal bimolecular mass-action systems with limit cycles},
author = {Balázs Boros and Josef Hofbauer},
journal= {arXiv preprint arXiv:2202.11034},
year = {2023}
}