Calculation of Separatrices in Multistable Chemical Reaction Systems

Abstract

In multistable chemical reaction systems the space of variables is partitioned by separatrices into different cells which are the domains of attraction of the respective critical points. By numerically solving an initial value problem, which is based on the particular stability properties of separatrix manifolds, we achieve a direct approximation of the stability boundaries in the phase space. The method is principally applicable to nonlinear systems of any number of variables and, other than the direct method of Liapunov, also in regions of the phase space which are far from the critical points.