The inheritance of local bifurcations in mass action networks

Abstract

We consider local bifurcations of equilibria in dynamical systems arising from chemical reaction networks with mass action kinetics. In particular, given any mass action network admitting a local bifurcation of equilibria, assuming only a general transversality condition, we list some enlargements of the network which preserve its capacity for the bifurcation. These results allow us to identify bifurcations in reaction networks from examination of their subnetworks, extending and complementing previous results on the inheritance of nontrivial dynamical behaviours amongst mass action networks. A number of examples are presented to illustrate applicability of the results.

References in corpus (6)

• 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
• Bifurcations in planar, quadratic mass-action networks with few reactions and low molecularity
• The smallest bimolecular mass-action system with a vertical Andronov-Hopf bifurcation
• Deficiency of chemical reaction networks: The effect of operations that preserve multistationarity and periodic orbits