# The Inheritance of Local Bifurcations in Mass Action Networks

## TL;DR

This paper explores how certain dynamic behaviors in chemical reaction networks can be inherited when the networks are expanded.

## Contribution

The paper introduces a method to identify bifurcations in reaction networks by examining their subnetworks.

## Key findings

- Enlargements of mass action networks can preserve local bifurcations under a transversality condition.
- Bifurcations can be inherited from subnetworks, extending previous results on dynamical behavior inheritance.
- Examples demonstrate the practical applicability of the inheritance results.

## 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.