STEADY STATE MULTIPLICITY ANALYSIS OF LUMPED-PARAMETER SYSTEMS DESCRIBED BY A SET OF ALGEBRAIC EQUATIONS

Abstract

The mathematical models of many lumped-parameter chemically reacting systems consist of a set of algebraic equations which cannot be reduced explicitly to a single equation. We describe here the Liapunov-Schmidt procedure which reduces the prediction of the local multiplicity features of a system of algebraic equations to the analysis of the features of a single equation, even though the original set of equations cannot be reduced to a single equation. This reduction enables the systematic analysis of a class of problems which could not be handled previously. Several examples illustrate the application of this procedure. A special reduction procedure is presented for systems described by a set of polynomial equations. The reduction in these cases is easier to carry out and enables prediction of the global multiplicity features of the system.