Normal forms for chemical reaction systems via the affine transformation

✍ Scribed by G. Lyberatos; B. Kuszta; J.E. Bailey

• Publisher: Elsevier Science
• Year: 1985
• Tongue: English
• Weight: 867 KB
• Volume: 40
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(85)80059-2

✦ Synopsis

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, and G, 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.