Bifurcations and Singularities of Algebraic Differential Equations (BISADE)

Abstract

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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.

 


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Activities

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

                        undefinedThe Quantifier Elimination Aspect (Thomas Sturm)  

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

                          

 


Publications

 
Hassan Errami, Markus Eiswirth, Dima Grigoriev, Werner M. Seiler, Thomas Sturm, and Andreas Weber
In: Journal of Computational Physics (2015), 291(279-302)
 
 
Dima Grigoriev and Andreas Weber
In proceedings of Computer Algebra in Scientific Computing - 14th International Workshop (CASC 2012), Maribor, Slovenia, Springer, Sept. 2012
 
Hassan Errami, W. M. Seiler, Markus Eiswirth, and Andreas Weber
In proceedings of Computer Algebra in Scientific Computing - 14th International Workshop (CASC 2012), Maribor, Slovenia, Springer, Sept. 2012
 
Satya Samal, Hassan Errami, and Andreas Weber
In proceedings of Computer Algebra in Scientific Computing - 14th International Workshop (CASC 2012), Maribor, Slovenia, Springer, Sept. 2012
 
Hassan Errami, W. M. Seiler, Thomas Sturm, and Andreas Weber
In proceedings of Computer Algebra in Scientific Computing - 13th International Workshop (CASC 2011), Kassel, Germany, pages 135-143, Springer, Sept. 2011
 
 
N. N. Vassiliev (Editors)
Hassan Errami, Thomas Sturm, and Andreas Weber
In proceedings of Polynomial Computer Algebra, Saint Petersburg, pages 25-28, The Euler International Mathematical Institute, Apr. 2011
 
 
In: Bulletin of Mathematical Biology (Apr. 2011), 73:4(899-917)
 
 
Vladimir P. Gerdt, Wolfram Koepf, E. W. Mayr, and E. V. Vorozhtsov (Editors)
Andreas Weber, Thomas Sturm, W. M. Seiler, and Essam O. Abdel-Rahman
In proceedings of Computer Algebra in Scientific Computing - 12th International Workshop (CASC 2010), Tsakhkadzor, Armenia, pages 267-279, Springer, Sept. 2010