Sebastian Walcher, Reaction networks: Reduction of dimension and critical parameters

Abstract: Typically, the mathematical description of reaction networks involves a system of parameter-dependent ordinary differential equations. Generally, one is interested in the qualitative and quantitative behavior of solutions in various parameter regions. In applications, identifying the reaction parameters is a fundamental task. Reduction of dimension is desirable from a practical perspective, and even necessary when different timescales are present. For biochemical reaction networks, a classical reduction technique assumes quasi-steady state (QSS) of certain species. From a general mathematical perspective, singular perturbation theory – involving a small parameter – is often invoked. The talk is mathematically oriented. The following points will be discussed: Singular perturbation reduction in general coordinates. (“How does one compute reductions?”) Critical parameters for singular perturbations. (“How does one find small parameters?”) Quasi-steady state and singular perturbations. (“What is applicable, what is correct?”)