Abstract
Many chemical reaction systems may be described by a system of ordinary differential equations. In general, a nonlinear change of variables is required to transform a system model to a much simpler equation called the normal form, which retains all important local nonlinear features of the system. For systems with a single nonlinearity, an affine transformation that retains the original steady-state and eigenvalue structure brings the system to a much simpler form, the companion normal form, which in the cases of two- and three-dimensional systems is shown to coincide with the classical F 1 and G 1 bifurcation normal forms that are based on Jordan block structure. The theory is applied to establish the properties of a general allosterically regulated enzymatic reaction sequence and of an isothermal catalytic reaction system.
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