The inheritance of local bifurcations in mass action networks

TL;DR

This paper studies how local bifurcations in chemical reaction networks with mass action kinetics can be inherited by subnetworks, providing criteria to identify bifurcations through network extensions and illustrating with examples.

Contribution

It introduces a method to determine the inheritance of bifurcations in mass action networks by analyzing network enlargements under transversality conditions.

Findings

Bifurcations can be inherited by certain network enlargements.

Subnetworks can reveal bifurcation behavior of larger networks.

Examples demonstrate practical applicability of the inheritance criteria.

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.