Application of algebraic methods to the calculation of steady states in continuous culture

Abstract

For the calculation of steady states in continuous culture and the application to optimization, numerical methods for solving the related nonlinear system of equations are usually employed. Such a system may have more than one solution butnumerical algorithms find — at best — one solution per computational run depending on the starting point. There is no proof that all the solutions are actually found. To overcome these problems algebraic methods can be employed. Many biotechnological models can be transformed into a polynomial form. In contrast to nonlinear systems in general, polynomial systems are well investigated and all solutions can be calculated with given accuracy for example by using the Gröbner Bases representation. This allows even for sensitivity studies which are difficult to handle with numerical methods. The process of transforming and solving the system of equations is automated with the computer algebra system REDUCE. In this contribution the approach is presented and examples are shown.