Some minimal bimolecular mass-action systems with limit cycles. (August 2023)

• Record Type: Journal Article
• Authors: Boros, Balázs; Hofbauer, Josef
• Is Part Of: Nonlinear analysis. Volume 72(2023)
• Publication Date: 2023-08
• Subjects: Bimolecular network -- Competitive system -- Permanence -- Limit cycle -- Andronov-Hopf bifurcation -- Focal value; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2023.103839
• Languages: English
• ISSNs: 1468-1218

Abstract

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 these 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.