Using the blow-up technique for a modified Lindemann mechanism

Abstract

We study a modified Lindemann mechanism, in which the second part of the reaction is $$2B\rightarrow P$$ instead of $$B\rightarrow P$$ . This model gives rise to a degenerate singularity in the associated system of ordinary differential equations. Using the blow-up technique, we describe this singularity qualitatively, showing that there is an invariant line, and that in the first quadrant (where the reaction takes place), it is stable. As a consequence, numerical methods for integrating differential equations can be used with confidence. Several examples are included.