A dynamical systems model of the limiting oxygen index test

(Received Novembe 29r , 1998; revised February 2, 1999)AbstractOxygen index methods have been widely used to measure the flammability of polymericmaterials and to investigate the effectiveness of fire-retardants. Using a dynamical systemsframework we show how a limiting oxygen index can be identified with an appropriatebifurcation.The effectiveness of fire-retardants in changing the limiting oxygen index is calculated byunfolding the bifurcation point with a suitable non-dimensionalised variable whic, h dependsupon the mode of action of the additive. In order to use this procedure it is essential themodel is non-dimensionalised so as to retain the variables of interest as distinct continuationparameters.