Global analysis of the multiplicity features of multi-reaction lumped-parameter systems

Abstract Mathematical models of lumped-parameter systems in which many chemical reactions occur simultaneously contain a large number of parameters, so that a p Theoretical guidance is needed to determine all the multiplicity features and the corresponding parameter regions. A systematic, efficient scheme is presented for finding parameter values corresponding to a specific number of solutions. A new scheme is developed for bifurcation diagrams, which describe the dependence of a state variable on a slowly changing operating variable. Some general predictions are made abou systems. Bounds on the values of the bifurcation or state variable may create bifurcation diagrams which cannot be found close to the highest order sin of solutions even when an isola variety does not exist. Several examples illustrate the application of the mathematical techniques.