Global sensitivity analysis of nonlinear chemical kinetic equations using lie groups: I. Determination of one-parameter groups

We introduce one-parameter groups of transformations that effect wide-ranging changes in the rate constants and input/output fluxes of homogeneous chemical reactions involving an arbitrary number of species in reactions of zero, first and second order. Each one-parameter group is required to convert every solution of such elementary rate equations into corresponding solutions of a one-parameter family of altered elementary rate equations. The generators of all allowed one-parameter groups are obtained for systems withN species using an algorithm which exactly determines their action on the rate constants, and either exactly determines or systematically approximates their action on the concentrations. Compounding the one-parameter groups yields all many-parameter groups of smooth time-independent transformations that interconvert elementary rate equations and their solutions.