Special Topics in Ordinary Differential Equations: Symmetries and Reduction

What it is about

You engage with parameter-dependent ordinary differential equations (analytic or polynomial), their symmetries and special reduction methods. A focus lies on algorithmic/reconstructive methods for determining symmetries and critical parameters as well as applications in simple biochemical reaction networks. In the end you will be able to recognize symmetries, perform reductions and identify critical parameters for singular perturbations.

What you will be able to do

• Understand parameter-dependent ordinary differential equations
• Recognize and compute (infinitesimal) symmetries
• Perform symmetry-based reductions
• Apply singular perturbation theory (Tikhonov, Fenichel) and coordinate-free reductions
• Identify critical parameter values by algebraic methods (e.g. Gröbner bases)
• Apply the theory to simple chemical reaction networks (including Deficiency Zero Theorem)

What the module consists of

• VorlesungPresentation of theory, demonstrative examples and discussion
• Übung/Diskussion im PlenumEncourages own analyses and in-depth study of the literature

Teaching method

• Vorlesung (Tafel/Slides)Introduction to concepts, presentation of examples and methods
• Diskussion mit StudierendenPromotes independent analysis and deepened understanding