Limit cycles in mass-conserving deficiency-one mass-action systems

Abstract

We present some simple mass-action systems with limit cycles that fall under the scope of the Deficiency-One Theorem. All the constructed examples are mass-conserving and their stoichiometric subspace is two-dimensional. Using the continuation software MATCONT, we depict the limit cycles in all stoichiometric classes at once. The networks are trimolecular and tetramolecular, and some exhibit two or even three limit cycles. Finally, we show that the associated mass-action system of a bimolecular reaction network with two-dimensional stoichiometric subspace does not admit a limit cycle.

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Cited by in corpus (4)

• The smallest bimolecular mass action reaction networks admitting Andronov-Hopf bifurcation
• Oscillations in three-reaction quadratic mass-action systems
• Some minimal bimolecular mass-action systems with limit cycles
• The smallest bimolecular mass-action system with a vertical Andronov-Hopf bifurcation