Oxygen index methods have been widely used to measure the flammability of p
olymeric materials and to investigate the effectiveness of fire-retardants.
Using a dynamical systems framework we show how a limiting oxygen index ca
n be identified with an appropriate bifurcation.
The effectiveness of fire-retardants in changing the limiting oxygen index
is calculated by unfolding the bifurcation point with a suitable non-dimens
ionalised variable, which depends upon the mode of action of the additive.
In order to use this procedure it is essential the model is non-dimensional
ised so as to retain the variables of interest as distinct continuation par
ameters.