Disjoint bifurcation diagrams in combustion systems

It is shown that the classical non-dimensionalisation of many simple combusting systems is sufficiently nonlinear to conceal some of the differences in behaviour shown when different bifurcation parameters are varied quasi-statically to produce bifurcation diagrams. Variations of ambient or feed temperature, in particular, can produce a bifurcation diagram where the upper stable state is on a branch which is disjoint from the rest of the diagram, indicating that the combustion state cannot be extinguished by lowering this temperature to any physically attainable level.