A dynamical systems model of the limiting oxygen index test

Oxygen index methods have been widely used to measure the flammability of polymeric materials and to investigate the effectiveness of fire-retardants. Using a dynamical systems framework we show how a limiting oxygen index can 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-dimensionalised variable, which depends upon the mode of action of the additive. In order to use this procedure it is essential the model is non-dimensionalised so as to retain the variables of interest as distinct continuation parameters.