Bifurcations and Singularities of Algebraic Differential Equations

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 differential 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 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 (DAEs), 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 environment.

DFG-Verfahren Schwerpunktprogramme

Teilprojekt zu SPP 1489:  Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory