# Bifurcations and Singularities of Algebraic Differential Equations (BISADE)

## Abstract

## Details

- Funding: German Research Foundation (DFG)
- Participating researchers:

## Description

We will analyse bifurcations and singularities of algebraic systems of ordinary differential equations with particular emphasis on questions concerning the existence of oscillations. Exploiting previous results that the study of bifurcations for normal systems of ordinary equations leads to questions in real algebraic geometry, we will develop efficient algorithmic methods for parametric bifurcation analysis and use them both for experimental mathematical investigations of low dimensional systems and for "real world applications" like the analysis of controllers for humanoid locomotions or the the analysis of chemical reaction systems of non-trivial size. Then we will extend these results to non-normal systems, i.e.to differential algebraic equations (DEAs), and study both the effect of singularities on bifurcations and the relationship between bifurcations of DAEs and singularities of associated systems of partial differential equations. Another major goal consists of making all the developed algorithmic methods available in an integrated form in a common software einvironmement.

## Activities

##### Workshop: Algebraic Geometry and Stoichiometric Network Analysis (Kassel, Nov 2010)

**Participants:**Werner M. Seiler, Ralf Markus Eiswirth, Andreas Weber, Vladimir Gerdt, Thomas Sturm, Hassan Errami

**Slides:**Algebraic Geometry and chemical Dynamics (Markus Eiswirth)

The Quantifier Elimination Aspect (Thomas Sturm)

Algorithmic semi-algebraic methods for computing Hopf bifurcation (Andreas Weber)

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